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/5478637Round 2:
https://www.behindthename.com/bb/game/5478642Round 3:
https://www.behindthename.com/bb/game/5478783Round 4:
https://www.behindthename.com/bb/game/5478847Round 5:
https://www.behindthename.com/bb/game/5479007----
Round 6: Child 2 has one kid and Child 3 has one kid!
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): Mark Faramund Theodore Simeon Lucio Matteo Isaiah Damian Anton Christopher
girl names (d10x2, reroll if same): Nessa May Leila Bryony Primrose Samantha Ariadne Kirsten Alanis Elissa
jobs (d6, no reroll): documentary journalist, vegetable farmer, painter, potter, restaurant manager, photographer
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)