Sorted by the four symbolic elements. Some names, like bright/shining names and musical names, could fit in air/fire or air/water respectively, so there is some overlap.

GIRLS

AIR

• Aine - Irish - Brightness, splendor
• Albina - Latin - White, bright
• Amaryllis - Greek – Sparkling
• Aria – Italian – Air; song or melody
• Arianwyn - Welsh - White, holy silver
• Aster - Greek – Star
• Astra - Greek/Norse/Latin - Star, divine strength, of the stars
• Aurora – Latin – Dawn
• Calliope - Greek - Beautiful-voiced
• Celeste - French/Latin - Celestial, heavenly
• Chiara - Italian - Bright, clear, famous
• Circe - Greek – Bird
• Dawn - Old English - The first appearance of light, daybreak
• Dove - English – Bird
• Electra - Greek - Sparkling, shining, bright
• Elide - Latin - Small, winged
• Esther - Persian - Star
• Fiona - Gaelic - White, fair
• Guinevere - Old French diminutive of Welsh Gwenhwyfar - Fair, white, smooth
• Helena - Greek – Bright, torch, light(see: fire)
• Hester - Persian - Star, varation of Esther
• Iridessa - English - Iridescent, light, illuminated
• Lenore - Diminutive of Elenore - Light, torch, bright (see: fire)
• Leora - Hebrew - Light unto me, I have light
• Lilette - Hebrew - Lady air, goddess of the south wind
• Lucinda - Latin – Illumination
• Lucy - English/French - Born at dawn, daylight, light
• Lyra - Greek – Lyre
• Medea - Greek - To ponder, cunning
• Melody - Greek - Song
• Minerva - Latin - Of the mind, intellect
• Nephele - Greek – Cloud
• Paloma - Latin - Dove, peaceful
• Piper - English - One who plays the pipe
• Raven - English - Colour, Bird
• Roxanna - Persian - Little star
• Roxanne - English/French - Dawn, bright, radiant one
• Sky - English - Word name
• Sorcha - Irish - Bright, shining
• Stella - Latin/Italian – Star
• Tindra - Swedish - To twinkle or sparkle
• Vanessa - English - Literary invention, butterfly
• Veda - Sanskrit - Knowledge, wisdom
• Wren - Old English – Bird
• Zosia - Polish - Wisdom

FIRE

• Amber - Arabic – Jewel
• Aria – Albanian/Hebrew – From gold; Lioness of God
• Aurelia - Latin – Golden
• Brighid - Irish - Strength or exalted one; Mythological goddess of fire, poetry, and wisdom
• Ember - English - Spark, burning low
• Fiamma - Italian - Little flame
• Fiammetta - Italian - Little flame
• Harper - English - Harp player
• Helena - Greek – Bright, torch, light
• Helia - Greek - Sun ray, of the Sun
• Lenore - Diminutive of Elenore - Light, torch, bright
• Marceline - Latin - Dedicated to Mars
• Marcelle – French – Warlike
• Orla - Irish - Golden princess
• Phoebe - Greek – Bright; name for Artemis
• Ruby - Latin - Deep red precious stone, gemstone
• Scarlett - English - Scarlet, red
• Serafina - Latin/Hebrew - Ardent one, burning ones
• Sol - Spanish – Sun
• Solveiga - Old Norse - Strong house or sun's path
• Sterope - Greek - Flash of lightning, lightning
• Vesta - Latin -To stay, dwell, Roman Goddess of the hearth

WATER

• Aerwyna - English - Friend of the sea
• Asherah - Semitic - Goddess of motherhood & fertility, lady of the sea
• Calliope - Greek - Beautiful-voiced
• Coralie - Latin/French – Coral
• Coraline – Latin – Coral
• Cordelia - Latin/Celtic/French - Heart, jewel of the sea, heart of a Lion
• Cynthia - Greek - From Mount Cynthus, moon Goddess
• Delphine - French – Dolphin
• Elendra - Sanskrit - Home by the sea
• Ginevra - Italian - White wave, fair one
• Gretel - German – Pearl
• Greta - German – Pearl
• Harper - English - Harp player
• Isolde - Welsh - Ice ruler
• Lorelei - German – Temptress (siren)
• Luna - Italian/Spanish/Romanian/Latin - The Moon
• Maggie - English – Pearl
• Maisie - Scottish - Diminutive of Mairead, pearl
• Marion - French diminutive of Marie - Sea of bitterness, mistress, lady of the sea
• Marjorie - Diminutive of Margaret – Pearl
• Melody - Greek - Song
• Morgan - Celtic/Welsh - Sea-born, sea-song, sea-circle
• Morgana - French - Sea-circle
• Morwenna - Welsh - Maiden, sea wave
• Muirgen - Gaelic - Born of the sea
• Naida - Greek - Water Nymph
• Nixie - Old German - Water sprite
• Ondine - Latin - Little wave
• Rita - Hindi – Pearl
• Rosemary - Latin - Rosemary plant, dew of the sea
• Selene - Greek – Moon
• Tallulah - Choctaw/Irish - Leaping water

EARTH

• Acacia - Greek - Thorny
• Acantha - Greek - Thorn, prickle
• Ardith - Hebrew - Flowering field
• Azalea - English - A flower
• Belinda - Italian/German - Beautiful, bright serpent, bright linden tree
• Blossom - English - To thrive, flourish
• Bluebell - English – Flower
• Bryony - Greek - To sprout
• Daffodil - Dutch – Asphodel
• Dahlia - Hebrew - Flowering branch
• Daisy - Old English - Day’s eye
• Daphne - Greek - Laurel tree, bay tree
• Demetria - Greek - Follower of Demeter
• Diantha - Greek - Divine flower
• Ebony - English - Deeply black wood
• Elowen - Cornish - Elm tree
• Esme - French - Esteemed, beloved, Emerald
• Esmeralda - Spanish – Emerald
• Evanthe - Greek - Fair flower
• Fauna - English - Young Deer
• Fern - Old English - Plant
• Fleur - French - Flower
• Flora - Latin - Flower
• Forsythia - English - Forsyth’s flower
• Freesia - German - Freese’s flower
• Gaia - Greek – Earth
• Gardenia - Scottish - Garden’s flower
• Hadassah - Hebrew - Myrtle tree
• Halley - Old English - Hall, large house, woodland clearing
• Hazel - Old English - Hazel tree, colour
• Holly - Old English - Holly tree, to prick
• Hortensia - Ancient Roman - Of the garden
• Hyacinth - Greek - Blue flower
• Hydrangea - Greek - Water barrel, flower
• Iolanthe - Greek - Violet flower
• Iris - Greek - Rainbow, flower
• Isla - Spanish/Scottish – Island
• Ivy - Old English - Evergreen climbing vine
• Jade - Spanish - Precious green stone
• Jasmina - Arabic - Jasmine, beautiful, flower
• Jessamine - Persian - Jasmine, beautiful, flower
• Juniper - English - Juniper tree, berry
• Kezia - Hebrew - Cassia tree
• Laurel - Latin - Laurel tree
• Lavender - English - Flower, colour
• Lilac - English - Flower, colour
• Lilou - French - Lily, flower
• Lotus - Greek - Lotus flower
• Magnolia - Latin - Magnolia tree, great, splendid beauty, dignity
• May - Latin - Month, Maia Greek Goddess of increase
• Meadow - Old English - A mown field
• Minerva - Latin - Of the mind, intellect
• Myrtle - English - Evergreen shrub
• Nesrin - Persian/Iranian - Wild rose, sweetbrier
• Olive - English - Olive tree, colour
• Petal - Greek – Leaf
• Petra - Greek - Stone, rock
• Poppy - Latin - Red flower
• Prairie - French - Meadow, pasture
• Primrose - Latin - First rose
• Qetsiyah - Hebrew – Cassia
• Rhoswen - Welsh - White rose
• Roisin - Irish - Little rose
• Rose - Latin - Rose, flower
• Sakura - Japanese - Cherry blossom
• Sylvie - French - from the forest, variation of Latin Sylvia
• Tabitha - Aramaic – Gazelle
• Tamara - Hebrew - Palm tree
• Tawny - Irish - A green field, golden brown
• Terra - Latin - The planet Earth
• Tess - Greek - Harvester, to reap
• Tulip - Turkish/English - Turban, flower
• Ursula - Latin - Little female bear
• Violet - Latin - Purple, flower
• Viorica - Romanian – Bluebell
• Waverley - English - Meadow of quivering Aspens
• Willow - English - Willow tree
• Wisteria - English - Wister’s flower

BOYS

AIR

• Armon - Hebrew - High place
• Bertram - German - Bright Raven
• Bram - Dutch - Raven
• Breeze - English - Soft wind
• Callum - Scottish/Gaelic - Dove
• Castor - Greek - To excel, shine
• Evren - Turkish - Cosmos, the universe
• Ewan - Scottish/Gaelic - Born of the mountain
• Finn - Irish - Fair, white
• Finnegan - Irish - Fair, white
• Guthrie - Irish - Windy place
• Hawke - Old English - Hawk, Bird
• Hugo - German/Spanish/Portuguese - Mind, spirit
• Icarus - Greek - Mythology name
• Ingram - German - Ing’s Raven
• Jules - French/Latin - Youthful, soft
• Julian - Latin - Youth
• Julius - Latin - Youth
• Lark - English - Bird
• Luca - Italian - Bringer of light
• Lucius - Latin - Light
• Orestes - Greek - He who stands on the mountain
• Orion - Greek - Dweller on the mountain, dawn, east; constellation
• Piper - English - One who plays the pipe
• Poe - English - Peacock
• Puck - English - Mischievous Fairy
• Remington - Old English - Raven, settlement
• Sage - Latin - Wise, herb, prophet
• Skye - Scottish/English - Protection, scholar
• Talon - French - Large claw of a bird of prey
• Zephyr - Greek - West wind, Greek God of the west wind

FIRE

• Aries - Latin - Ram
• Auburn - English - Reddish brown, colour
• Bayard - English - Russet-haired
• Cinder - English - Ash, ember
• Cyrus - Greek/Persian - Sun
• Dandelion - English/French - Lion’s tooth (Dent de lion)
• Flavius - Latin - Golden, yellow-haired
• Flynn - Irish - Red, reddish
• Icarus - Greek - Mythology name
• Ignatius - Latin - Fiery one
• Kyros - Persian - Sun
• Leo - Latin - Lion
• Marcel - French - Little warrior
• Phoenix - Greek - Dark red
• Pine - English - Pine tree
• Rory - Scottish/Irish - Red King
• Rowan - English/Scottish/Celtic - Red-haired one
• Rufus - Latin - Red-haired
• Ruslan - Slavic - Lion

WATER

• Alpheus - Greek - River God
• Calder - English/Scottish - Rough waters, stream
• Dagan - Hebrew - Earth, grain, little Fish
• Halloran - Irish - Male descendant of a pirate or stranger from overseas
• Kai - Japanese/Swedish - Ocean, shell, restoration, recovery, rejoice
• Kellan - German/Irish - Swamp, slender
• Lake - English - Body of water
• Link - English - Town by the pool
• Maxwell - Scottish - Great stream
• Merlin - Welsh - Sea fortress
• Mortimer - English - Dead sea
• Ocean - English - The ocean
• Ren - Japanese - Water lily, Lotus
• Ronan - Irish - Little Seal
• Struan - Gaelic - Stream
• Yarrow - English - Rough stream

EARTH

• Alder - English - Alder tree
• Arden - Latin - Great forest
• Arthur - Celtic - Bear
• Aspen - English - Aspen tree
• Beowulf - English - Bee Wolf
• Birch - English - Birch tree
• Blair - Scottish - Plain, field, battlefield
• Briar - English - Thorned shrub
• Bromley - Old English - Woodland clearing where broom grows
• Caledon - Irish/Latin - Hard or rocky land
• Cedar - English - Cedar tree
• Cephas - Aramaic - Rock
• Conan - Iris - Little Wolf, little hound
• Copper - English - Metal, colour
• Cypress - Greek/English - Cypress tree
• Dagan - Hebrew - Earth, grain, little Fish
• Dmitri - Greek - Earth-lover, of Demeter
• Ewan - Scottish/Gaelic - Born of the mountain
• Fenrir - Old Norse - Fen-dweller, Fenrir’s Wolf
• Figg - English variant of Fig - Fig tree
• Finnick - English - Marshland farm
• Florent - French - Flowering
• Florian - Latin - Yellow, blond, flowering
• Forrest - English - Variant of Forest, dweller near the woods
• Fox - Old English - Fox, animal
• Gable - Old Norse - A triangular-shaped hill
• Garland - Old English - Triangle land
• Hawthorne - English/Scottish - Someone who lives by a bush or hedge of Hawthorn
• Huckleberry - English - Sweet berry
• Lachlan - Scottish - from the fjord-land
• Leaf - Old English - Dear, beloved, foliage
• Leland - Old English - One who lives near a clearing or piece of fallow land
• Linden - English - Linden tree hill
• Marley - Old English - Pleasant wood, from the lake meadow
• Moose - German/English - Moss, animal
• Moss - English - Nature name
• Oleander - English - Evergreen shrub
• Oliver - Latin - Olive tree
• Orestes - Greek - He who stands on the mountain
• Orion - Greek - Dweller on the mountain, dawn, east; constellation
• Orson - English - Bear cub
• Oscar - English/Irish - God spear, deer-lover, champion warrior
• Pyrus - English - Fruit trees
• Ramsey - English - Low-lying land
• Sidney - Old English - Wide meadow
• Silas - Latin - Of the forest, God of trees and forests
• Silvan - Latin - Of the forest
• Silvius - Latin - Wood forest
• Slate - English - Gray-green rock
• Sylvester - Latin - Wooded, wild, woodland
• Syrin - Norwegian - Lilac
• Ulric - Old English - Wolf power
• Vernon - English - Alder tree grove
• Wolf - English - Animal
• Wolfgang - German - Path of the Wolf
• Wulfric - English - Wolf, rich, powerful
• Zev - Hebrew - Wolf