That’s exactly how my pets get named. They tell me. Usually it takes days to a week, however I had one cat that took three weeks to let it be known.
I had a dog that would not answer to any name I gave her. I had her on my lap one day about a month after I got her and I asked her what her name was. We were eye to eye. She looked at me and projected “Kitty.”
When next I called her, I said, “Here, Kitty!” I’m sure her previous owners had catz and “Here, Kitty” was the signal for food. She weighed four pounds and I loved her silly self!