Great idea. Thanks for sharing, and congrats on launching it!
As someone unfortunately prone to coming up with grand plans to build things, I could get a lot of use out of this. I have a handful of domains currently collecting dust, but hope to actually follow through on my plans at some point :) Far more time than I'd care to admit was spent on finding them, so something like this would have been a great time saver.
The most important feature IMO is the .com availability checking, which doesn't seem to be working at the moment. In addition to the AI-generated names, it might be nice to allow users to enter names manually as well (once I see an AI generated one, by brain starts to generate lots of similar ideas). Another cool feature could be to be able to select a domain you like, and then have it generate further suggestions similar to that name.