We know a cat by any other name would still smell as… cat-like, but we still think names are pretty important. Your cat's name gives him a certain air, and gives you a certain way of addressing him. There's a big difference between a name like Sir Snufflebottom and Bob, is what we're saying.
As poet T.S. Eliot and the musical "Cats" point out, "the naming of cats is a difficult matter" (but more on T.S.Eliot later!). In fact, the musical and the work is was based on point out that every cat has three names: his given name, the name you actually use to call him, and a secret name that only the cat himself will ever know.