Sorry, for some reason I felt it needed a more elaborate explanation.
No, I take that back, you wrote;
...He wanted to call himself Fats Domino, only Fats got there first...
...Seriously, that's why he's called Chubby Checker. Someone at Cameo-Parkway thought he sounded and looked a bit like Fats, and anyway it's a catchier name than his real one, Ernie Evans...
which is not the same thing at all.
Anyhow, I think my explanation sounds better.