Question: I need a tool that generates business name ideas and checks for domain name availability.

If you're looking for a tool that can come up with business name ideas and check domain name availability, Namify is a good choice. This AI-powered tool will generate more than 1,000 business name ideas based on your input, and it'll check for availability of the domain name, social media username and trademark. That means you can find a brandable name that works for your business without worrying about stepping on someone else's toes. Namify also offers free logo options if you buy domain names through some extensions, so you can get a good online presence without a lot of extra hassle.

Another option is Namelix, which uses large language models to come up with short, brandable business name ideas. You can narrow down results by name length, specific keywords and domain extensions. Namelix will give you personalized recommendations based on your preferences, so it's a good option for new businesses that want a professional and relatively affordable identity without spending a lot of money.