Why is Ponyboy named Ponyboy?

Ponyboy's father actually gave him his name.

I wished she hadn't asked me that. I hate to tell people my name for the first time. "Ponyboy Curtis."
Then I waited for the "You're kidding!" or "That's your real name?" or one of the other remarks I usually get. Ponyboy's my real name and personally I like it.
The redhead just smiled. "That's an original and lovely name."
"My dad was an original person," I said. "I've got a brother named Sodapop, and it says so on his birth certificate."