Google's John Mueller was asked about if it is okay with Google Search to have a website with the same name as another site on the internet. John said he could not give legal advice around copyright issues but he said when it comes to Google Search and SEO, it is fine.
John was asked, "By chance, I discovered that there is a website that has the same name as mine, but its website address is different, the language of its website is different, and the topic of the website is different. Is this considered a violation of Google's laws?"
John replied, "There are lots of sites that have similar names (there are a lot of top level domains, so it happpens that someone uses the same "name" on a different top level domain). That's fine, there's no rule against it from us. I can't help with copyright or trademark (or other legal) issues, so if you think that's a problem, you'd be best off checking with a lawyer."
Yea, the issue would be more around legal issues and that would worry me more than the SEO or Google issues.
And if you want your website to come up first for your company name and someone more established uses that name, you might be out of luck as well.
In my opinion, change the name of your company if it is not too late.
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