The phylum name for fish is chordata. Members of this phylum all have a notocord, or a piece of cartilage that acts as a backbone, at some point in their lifecycle.
Scientists divide chordata into three smaller groups, called subphyla. The first of these is called vertebrata, and it includes fish. It also includes reptiles, amphibians, birds and animals. The other two subphyla are urochordata and cephalocordata. Urochordata includes marine animals like sea squirts that feed on small particles in the water and act as filters for the ocean environment. Cephalocordata includes lancelets, which are marine animals similar to fish.