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/5478783----
Round 4: name spouses for all 4 kids.
gender (d20):
19-20 = nonbinary
all other odd numbers = boy
all other even numbers = girl
boy names (d20x2, reroll if same): Amal Nathaniel Odin Alder Cedar Poseidon Cassiel Terence Gingko Khepri Silvio Merlin Gideon Paul Arthur Talon Falco Lachlan Victor Laurence
girl names (d20x2, reroll if same): Thea Selene Carmen Laura Thuja Oona Adriana Faith Kasia Gaia Phaedra Phoenix Asherah Chimalma Guinevere Nova Camilla Ianthe Tessa Malini
surnames (d8, reroll if same): Booker Soong Ramirez Davilla Fallon Compton Hossain Garduno
jobs (d12, no reroll): composer, gardener, carpenter, editor, illustrator, pilot, sign language interpreter, daycare teacher, pharmacist, journalist, software developer, pathologist
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)