Well, since jokes get funnier as you explain them, prepare for a hilarious adventure.

OP states that he thinks Chloe is inappropriate.
Why though. Chloe is a perfectly cromulent name.

The other chicken’s names are puns related to Stevie Chicks is a pun on Stevie Nicks, Princess Layer is a pun on Princess Layer.

Of course, this isn’t too hard to see.

Still, why does OP think Chloe is inappropriate?

Chloe is similar sounding to a chicken’s (cloaca)[en.wikipedia.org/wiki/Cloaca]. A comedian might call it a pussy-dick-butt.

Do you see how hilarious it is now that I’ve explained the joke. Gafaw gafaw.