In my exploration of OpenAI, I just created a domain-name search that takes business description as an input, and generates interesting domain names for it. It then uses DNSimple API to check if .com is available.
In my view it is a much easier way to find a suitable domain, as the AI thinks of a much large pool of possible names than my own brain. SmartyNames found its own name, using the tool itself.
Hope you enjoy it! https://smartynames.com/