Looking at the NPCs, tia seem to hold on to their Mother Tribe Letter until they are attempting to become a nunh. Nunh (as well as nunh hopeful) seem to use the tribe letter of their (for lack of a better word) wives.
of course, the only nunh hopefuls we know are from the U or M tribes and they are both rather odd, lore breaking tribes. And we don't have ANY in game tribe that follows the lore we were given for them so idk. :l

The way I see it, children belong to the tribe. So they would carry their mother's Letter. If male, they would hold onto that letter as they go out into the world. Then when they find a tribe they want to join, and have the ok to idk trial? for the role of Nunh they drop their Mother Tribe, and adopt the new tribe. If they succeed, congrats they're tribe daddy. If they fail, they probably go back to roaming, using their Mother Tribe Letter.

I think the only way a child would take on their Father's Tribe letter is if they were being raised alone by their father (the tragic back story of at least 1 npc) or their father established an offshoot or double letter tribe.