Like the original by @Iolanthe_Katerina, the game plays by someone saying what they would name twins, then the next person will say if they would also use the same names or would change them to something similar.
Example
P1: I would name twins [name_u]Elijah[/name_u] [name_m]Frederick[/name_m] & [name_u]Quinn[/name_u] [name_u]William[/name_u], would you?
P2: No, but I would name them [name_u]Elliott[/name_u] [name_u]Freddie[/name_u] & [name_u]Quinn[/name_u] [name_f]Wilhelmina[/name_f], would you?
P3: Yes, I would name twins [name_u]Elliott[/name_u] [name_u]Freddie[/name_u] & [name_u]Quinn[/name_u] [name_f]Wilhelmina[/name_f], would you?
P4: No, but I would name them [name_u]Eliot[/name_u] [name_u]Freddie[/name_u] & [name_f]Wilhelmina[/name_f] [name_u]Quincy[/name_u], would you?
Starting with…
I would name twins [name_f]Faye[/name_f] [name_f]Georgia[/name_f] & [name_u]Lyle[/name_u] [name_u]Benjamin[/name_u], would you?