Amy's daughter is River Song.
Amy named her daughter Melody Pond. When Lorna Bucket of the Gamma Forest embroidered the prayer leaf in "A Good Man Goes to War", she used her people's word for "song" as the translation of "Melody" and, because "the only water in the [Gamma] Forest is the river", she used "river" as the translation of "Pond". The names were on opposite sides of the leaf, so their order depends on which side you see first. Amy, Rory and company saw the surname first, then the forename -- so they saw the full name as "River Song". Paradoxically, Amy had chosen the name Melody, in the first place, because of her childhood friend Mels (short for Melody), who was actually the incarnation of River immediately before the incarnation played by Alex Kingston. Thus, as the Doctor pointed out to her, Amy had named her daughter after her daughter.