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The thing I find interesting is that doing the research gives me a new perspective on whether or not I really want to go after that business/model. The SEO search turns up potential competitors, domain squatters, etc. While thinking about different names to lookup and key words to search for, my context changes to a potential customer...
A lot of times it reminds me ("oh yeah... did I talk to real potential customers yet?") and if I didn't, I'm in real trouble of building another tool that no one wants :(
Consider the fact that a brand and the company name are two separate things. Think Uber Cab (Uber), Google (Alphabet), Tide (P & G). The domain name can/should be tied to the product - and the brand. The company name itself can be anything really. As a first step to a rename if you really really want to do it, you could file an incorporation document amendment that says "Company AD15asd Corp, d.b.a. NiceBrand"