Actually, it's perfectly normal to rename a pet when you adopt it. And, since you renamed your previous cats, and nothing bad happened because of that, why assume that something bad will happen now when you adopt a new friend for Tigger and rename it.

I"ve renamed past cats I've adopted and nothing bad ever happened as a result of that.

Animals don't respond to words, as much as they respond to the voice tone, inflection, and cadence. Yes, cats can recognize certain words that are used repeatedly if those words are said with the same tone, inflection and cadence. Cats also are smart enough to recognize angry versus happy tones of voice used with them. Animals are far smarter than humans give them credit for. Did you know, for example, that cats don't typically meow with each other, but they do so with humans to get our attention.

Cats are wonderful companions, especially for those of us who struggle with anxiety and depression. If I lived in a bigger space, I'd adopt a 2nd cat companion for my cat but she doesn't seem to mind being alone.

Try not to worry so much about changing your new cat's name, since you've done it before. Congrats on deciding to adopt another cat. They sure are great friends to have around.