In the Outsider's book written by S.E Hinton. How did Sodapop and Ponyboy get their names? Are they Nicknames?

From the text:

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."