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.
If you dream of adopting a stray cat, it means you’re being called upon to donate your services and resources to take care of a homeless living thing. In dream imagery, the cat is usually an icon/ symbol for a woman. In waking life, there could be someone female you know, who has primary needs, secondary needs, care, support and stability. Adoption fosters the unconscious hope of parental nurturing, and a happy forever home.
Chances are high that a stray cat (or human being) has received bullying, abuse and ill treatment. The cat symbolizes a domestic animal which must have come from a home, born from its domesticated mother.
The cat would have learned defensive mistrust as protection against the old learned behavior pattern of ill treatment.
The stray which was abandoned would have internalized old hate and it has learned it needs to be aware of old hateful situations which may surface anytime. In the early days of being re-homed, the adopted cat wants to learn what happens when the stimulus of hate appears in its new home.
If the adopter tolerates their hatred, especially after the cat does a misdeed, the animal knows that it is accepted by the new adopter. It will form an attachment bond with the adopter and accept them as someone it can trust.
