Your cat would be described as a black domestic longhair mixed breed, or "moggie" if you live in the UK. He or she is a very lovely cat. Cats are not really considered a breed unless they have a pedigree. You might find a black cat that is a specific breed that looks like your cat. You can do a google search for "black longhair cat photos" and see a lot of them. Some may belong to a breed but others will not.
She is pretty - I love longhaired cats. The vast majority of cats do not belong to a breed, and probably have no pedigree or 'breed' ancestors. It is the opposite to dogs, where every one has at least some breed ancestry that comes out in their looks and habits. This is because cats were not bred specifically until very recently - about 200 years ago, when people took different cats who had evolved differently in various parts of the world and began to choose types to breed from, so getting our modern 'breeds'. Most cats are just called 'domestic', though you can say that a longhair cat carries the gene that allows it to survive in a cold climate, so it must have ancestors from the Northern countries.