The idea is that you will generate a birthday for each family member, and use that to give them names that have that name day!
How many kids are in the family (roll a six-sided die: https://www.randomlists.com/dice?sides=6&qty=1):
1- 2
2- 3
3- 4
4- 5
5- 6
6- 7
Roll to see if there are any multiples (you can’t have triplets if you rolled a one last time, but you can have twins):
1- triplets
2- twins
3- no
4- no
5- twins
6- no
Now their genders (roll for each child):
1- Girl
2- Girl
3- Boy
4- Boy
5- Girl
6- Boy
Now ages (the parents’ ages are your choice and try to avoid having kids of the same age if they are not a multiple):
1- 0-2
2- 3-5
3- 6-8
4- 9-11
5- 12-14
6- 15-17
Now roll and record their birthday (year doesn’t matter, multiples have the same birthdays) (all you need to do is make sure Generate Life Story is clicked, gender does not matter): http://www.behindthename.com/random/?number=2&sets=1&gender=both&surname=&showextra=yes&usage_fntsg=1
And find the perfect combo with names from any of the countries that have that family member’s birthday as their name day! I think all the days have enough names for both genders, but if I’m wrong, just roll another birthday for that person.
Here are the name days: https://www.behindthename.com/namedays/
Surnames are optional.