This game will have a dice option and a choice option! You can decide to play one way or the other, or do both and compare your choice family vs. randomly generated family. You can also decide to do something like using the dice for genders but free choice for the names, as long as you're consistent (so whatever you do in round 1 is what you have to do for the whole game).
Dice if you're using them:
http://www.brockjones.com/dieroller/dice.htm----
Round 1:
https://www.behindthename.com/bb/game/5478637----
Round 2: name the couple's oldest 2 kids
DC1:
DC2:
gender (d20):
19-20 = nonbinary
all other odd numbers = boy
all other even numbers = girl
for nonbinary characters you can combine the namebanks and roll a d20
boy names (d10x2, reroll if same): Cerdic Theodoric Haakon Leonardo David Raphael Mathis August Jonah Alastor
girl names (d10x2, reroll if same): Willa Ivy Annabeth Francisca Elizabeth Jacqueline Helena Katherine Penelope Sylvia
jobs (d6, no reroll): philosophy professor, bartender, speech therapist, electrician, postal worker, psychologist
nicknames (d6, no reroll):
1= no nickname
2= obvious nickname
3= no nickname
4= non-obvious nickname
5= obvious nickname
6= silly or babyish nickname (only used by family)