As its name suggests, the Futaba (or "Twin Leaves") clan is all about duplicity. Members of this clan are much more fertile than those of other clans, and typically have children born in sets of two with each twin, hopefully, representing different parts that make up a whole. The ideal is a set of identical twins, in which the genetic similarity enables a more full merging of each part. However, because identical twins, while numerous in this clan, aren't guaranteed, various other techniques have been utilized to make up for this defect. Fraternal twins are still able to merge with ease, but supplemental techniques must be used to get the ball rolling. This is especially true for non-twin siblings who cannot cohesively merge and rely entirely on outside jutsu to maintain a single form. These pairs are significantly weaker than an identical twin pair, but with the right training can become stronger together than apart.
The unity between pairs is considered a sacred bond. As a result, their unified form is usually given a name of its own. This naming process is very important, and as a result most children are named a certain way purely in order to reach a cohesive conjoined name. For example: Umeko and Maiko to form Mameko. It is also not rare for members of this clan to call each unit by its conjoined name when getting the attention of both parties. (Shiori only does this when they are visiting family.)
The Futaba clan is very lax when it comes to marrying outside of the clan. In fact, marrying outside the clan is somewhat encouraged as a means of strengthening and adding to their clan's repertoire. Their genes carry over well, and their high fertility means that the highlights of their clan usually present themselves at least once each following generation. As a result, their clan is very diverse and there isn't a single branch of the family that is considered wholly "pure" with regards to the original bloodline. Even the Main Branch isn't genetically like it was at the beginning! Tetsuo and Masao's branch is the Main Branch and takes great pride in being the most genetically similar to their ancestors. This branch of the family is very particular about carrying on clan traditions and producing heirs. This particular branch also prefers that women marry Futaba men so that they do not discard their clan name upon marriage.
Birth order between a twin pair is only important because the oldest twin is the more dominant of the two in the conjoined form during battle. Conjoined names will most often have the first syllable of the oldest twin come before the syllables from the younger twin's name to reflect this, though this is not a rule that is rigidly enforced or considered of extreme importance among the family. In every other respect, birth order is unimportant. That is, except when it comes to the clan head.
The Main Branch consists of a twin pair and both of their families. Twins become clan head together and delegate clan affairs as a unit. The clan head is determined by the oldest twin pair born between their families. It it not necessary for both twin pairs to get married, but if both become married, either one of them have the potential to produce a clan head pair. Birth order between the clan head pair does NOT determine whose kids are eligible to become clan heirs, no matter what Tetsuo's grandfather might say. It is very, very unusual for a twin pair in the main branch to be unable to provide a new twin pair for clan heir, as their genetics make them able to produce twins easily. In the event that this would happen, though, the oldest would become clan head upon succession regardless of status as a singlet or triplet+ set. Generally, though, members of the main branch produce offspring until a twin pair is achieved, so an event like this would be incredibly rare.