I just faced this with another startup wanting to use my name, plus their intended business is encapsulated as a feature in my startup. I was well over a year ahead of them, had already incorporated and started the Trademark process when I found them on Angel.co (which sadly doesn’t protect from reusing names). I talked to them directly, but they were pretty much jerks about the whole thing. Didn’t respect that I was still working on my startup and didn’t care about my Trademark.
After discussions with attorney’s and advisers, the simple answer is to just ignore the and build my startup.
If we both succeed, the name won’t matter and we can figure that out. If I succeed and they don’t, battle is over. Same for vice-versa.
It’s pointless to stress about this stuff. Just enact your vision and put all of your energy into doing so.