True, tried it so many times and every time I come up with something myself though sometimes inspired by the AI's ideas.

Verifying trademarks and domain name availability is usually an additional step you need to ask it to perform. Trademark DB searches by the way are intentionally made difficult to scrape so most of the time it's a manual process anyway.

However, once you give it all the information (TM search results, domain name availability) it can help you with the judgement of how safe the name is from the legal perspective. With the obvious caveats, but still a good starting point if you are serious about the name.