In the Doctor Who episode Let's Kill Hitler, Melody Pond doesn't know who River Song is. But in A Good Man Goes To War, it's explained that due to a translation error,
Melody Pond was raised under the name of River Song by the people who kidnapped her.
Based on what we know of her history, the opposite should have been the case, River Song shouldn't know the name Melody Pond.
We never learn Melody was raised under that name; only:
[River:] It’s your daughter’s name in the language of the forest. Except they don’t have a word for "pond" because the only water in the forest is the river. The Doctor will find your daughter, and he will care for her, whatever it takes. And I know that. It’s me. I’m Melody. I’m your daughter.
Note that she never actually says that Melody was raised there; only that that's how the name was derived. From that, River knows Melody's name from River's past; whereas Melody doesn't learn who River is until Let's Kill Hitler.
The following is from Let's Kill Hitler:
Furthermore, given that Amy names her daughter Melody after her own daughter, and that Melody only takes the name River Song after learning it from the Doctor and her parents, the true origin of both names is somewhat problematic (especially as to why exactly the universe decided she needed two names); then again, ontological paradoxes are nothing new to Doctor Who.
No... Amy names her daughter Melody after her best friend Melody. Pond is the last name. (Even though she's married - see the Big Bang episode.) The "River Song" thing is the translation that Lorna Bucket is forced into, because "there's no water in the forest except the river."
She was raised under the name Melody Pond. Madame Kovarian and cohort has no reason to know that the child becomes River Song, and so raises her as Melody Pond.
The only real question is how Melody herself doesn't know... Melody's been hearing stories from Rory and Amy about adventures with the doctor; she's got to have encountered River Song in those stories.
