Start selection of names directly from the object of your interest, that is, with cats. Of course, call the nursery is just "Cat" - not a good idea. But try to translate this word into other languages. For example, "Felis" ("cat" in Latin) is already quite adequate and harmonious name. You can play with the English name cat. My Cat, Cat World, and similar names, may not be so original, but will reflect your occupation.
Remember the famous cats that you know. For example, cartoon characters. Tom, kitten woof, Roger, Garfield can give your name to your nursery. Look for information about famous cats existed in reality. For example, the cat Larry, who has the proud title of Chief Mouser seat of Government of the United Kingdom, or the cat Scarlett, who at the Brooklyn fire 1996 pulled out of the fire of their own kittens. Why not give the kennel name that has some history?
If your kennel is to breed one breed, then concatenate the name with this breed. For example, if a cattery bred kittens, why not call it Britain or derived from this word? You can also beat any other breed of cats.
Give the nursery its name. However, this option is more suitable for women. The kennel name "Alexander" or "Angelica" might be to carry a few less semantic load than others, but it is beautiful.
Arrange a competition for the name of the kennel. It is best to hold such competitions among children. Ask people to suggest names, select the best ones and the winner will select some nice prize, for example, a soft toy cat.