OK, this is going to be VERY simple. All you have to do take the prefix of your favorite cat, and the suffix of your least favorite, or switch it.
For example, my favorite cat is Dovewing. So, the prefix would be Dove. My least favorite cat is Tigerstar, so the suffix would be star. My cat's name is... Dovestar!
Or, I could switch it, using Dovewing in the suffix and Tigerstar in the prefix, making Tigerwing. Pretty cool name, but I'd prefer Dovestar...