As I understood it, yes. Edit: Or not. In DW Confidential, the lady that plays River Song talked about the possibility that the Gallifreyan on the crib could have multiple names, or that the name had more of a meaning. It was pretty vague overall.
That was the crib that the Doctor had when he was a child, so it had his name on it. The crib that 'Melody' had was the high tech one that was sorta like a prison for the baby.
Even though it was kind of obvious compared to some of the other twists in Doctor who, I'm still excited to see what happens next with the storyline. It'd be interesting if it was still River Song who was in the astronaut suit that killed the Doctor later on, which would again explain her jail sentence for killing an important person.