A cat can recognize many owners in its lifetime. This is because cats have a very weak ability to recognize human faces; they mostly rely on voice and scent to distinguish people. Instead, they are more likely to recognize their home and environment.
How a cat behaves when it gets a new owner:
1. When a cat gets a new owner, it's also in a new environment. Some cats can't adapt at first and will often hide. But as they spend more time with their new owner, they will gradually open up and become happier in their new home. 
2. Some cats have a less clear memory of their owners. They only recognize whoever feeds them as their owner, so they can adapt quickly even if they have a new owner. This is common in kittens a few months old or cats with an optimistic and adaptable personality.
3. Some cats are very loyal, especially older cats that have lived with their owners for a long time. They prefer a stable and familiar living environment, and they have already memorized their owners, remembering everything from their scent to their voice. When such cats change owners, they often stop eating and drinking, and may eventually die of depression.
