I keep the first name, but I give the children last names based on their parents.

For example, Unagi and Lanu had a daughter they named Nunai, so
Nunai'ulan

Kwame and Okai had a son they named Kito, so Kito'okwam

Now, my villager Banga went and got pregnant without my knowledge, and she's been pretty tightlipped about the father of her son, Juro shares no known characteristics with any of the men, so I've named him
Juro'bson.

I sincerely hope I don't have this problem too much. I'm charting all the relationships to make sure no relatives breed with one another (at least to the 2nd degree).

Obviously, I put the game "on pause" overnight, or I'd have a village full of
Lulu'udotar and Hoto'bsons.