How can I do some testing to find a great name and domain for my startup?

I’ve been working on FormAPI (https://FormAPI.io) for over a year, but I’m not too happy with the brand. I’m working on a big redesign for the landing page and app, and I feel like it would be a good time to build a new brand.

Some people have been confused by “FormAPI”, because even after looking at the current homepage, they thought it was mostly about web-based forms. I’ve heard that the name / title is important for SEO, so I want people to find me when they search for “pdf generation API”, “generate PDFs”, etc. I have some new competitors that kicked me off the front page of search results because their domain is “pdfgeneratorapi.com”. So I think I need to at least get “PDF” in the new name.

I also have hunch that switching to the .com tld might give people slightly more confidence than io. (Even if it’s just a 5% improvement in conversions.) My target market is developers and technical managers, and I personally know that a .co or .io domain is often used by new startups, usually because they can’t afford a good .com domain. My service deals with a lot of very sensitive data and needs to be very reliable, so I need to work extra hard to convince people that they can trust the platform. (It’s the number one question I get in live chat support.)

I’ve come up with a long list of available .com domains that include PDF. I want to put a lot of effort into finding the optimal name, domain name, and logo, because I want to build this brand over the next 10 years. I’d also be happy to spend a few thousand dollars on a really great domain, but I’ve found lots of good options so I probably won’t need to do that.

What should I do next? I was thinking about paying some company to run a survey and ask people for their opinions on different names. Maybe rating qualities like “trustworthiness”, and things like that. But I’ve never done this before, so I’m not sure what to do. Thanks for your help!