I found this game on BabyNameGenie and really loved it, so I thought I'd bring it here! Here's the dice I use:
https://www.random.org/dice/
Roll 2 dice to determine how many children you have. Then roll for each gender, with odds corresponding to boys and evens corresponding to girls. Pull up your Spotify (or whatever music streaming service you use), choose a playlist, and put it on shuffle. The family member's first name is from the musician's name, and their middle name is from one of their songs. Last names are up to you. Have fun!