If you were dreaming of adopting a stray cat, it means you love cats in real life.
If you dream you were changing the name of the stray cat from a evil sounding name into a neutral / good name, it means you intend to make good out of a former bad life.
The dream interpretation is that you are going to help a cat or human to transition. The living thing may have a pathetic life before they met you. You intend to help transform its life. The dream of re-naming the living thing is a symbol of trying to make good after a bad past.