I'll suggest names for three siblings, two boys and a girl, that I think go well together. The next person gets rid of the first name and adds a name for the opposite gender that could go well with the other two. The next person does the same thing to the new set.
For instance, I could write Casen, Jayda, and Tyler. The next person might post Jayda, Tyler, and Bailey. The next might post Tyler, Bailey, and Brandon. The next might post Bailey, Brandon, and Breanna. And so on.
The first sib set:
Henry, Abigail, and Theodore.