Google's updates to its search engine algorithms nullified the impact of having domains that exactly match keywords, more commonly referred to as Exact Match Domain, abbreviated EMD.
Some argue there are still benefits to having keywords in a domain name if your site also meets Positive Engagement Metrics. But the purpose of the updates regarding EMD were to level the playing field with "domain farms" that would amass thousands of domain names based on keywords, while offering very little beneficial content to the public.
In your case, it so happens your startup's name, and variations of it, match many search results. It was unclear however from your question if the results returned will also match the content of your site (i.e., do they have similar information or services that you'll be providing).
If not, then your domain name would not be considered an EMD because the keywords in your site would not match your startup's name. In this case, the keywords in your site would return different search results, so there should be little reason to be concerned about the search results that your startup's name matches at this point (see "branding" below).
If the search results using your startup's name returned sites with similar content, that would be a different story. Again the domain name would not be factor, but if you use your startup's name in your content, as you likely would do, then you would be competing with those other search results based on that name alone, in addition to lots of other criteria Google uses to rank sites with. Also keep in mind that you'll likely have several keywords, and not just your name as a keyword.
Branding is also important to consider here: If you market your domain name as a brand, or the name itself becomes popularly associated with your service, then that might produce higher rankings for your domain. For example, if you type
Amazon into a google search, you'll see
amazon.com as the top results, instead of information about the Amazon Jungle, like you might have in the years prior to Amazon's branding success.
In general, you should worry more about picking good keywords that will match your site's content and offer the best quality content you can. On top of that, building brand identity is always a good strategy too. Since as you say, no one is doing business under the startup's name, then you should have an excellent opportunity to build a brand around it that both customers and search engines will start to recognize.