(Spoilers Main) Is Robb really Robert?

A friend of mine is an ASOIAF first time reader, and she asked me a question I can't answer. Is Robb Stark's full first name Robert? Or is it just Robb?

I guessed it was just Robb, as he's never referred to as Robert. But I have absolutely no idea why Catelyn/George made that decision.

Sorry to everyone who wanted a warging and/or time travel tinfoil theory based on the title.