That isn't how trademarks work. There can be multiple business with the same name, as long as they operate in a different field. Case in point, Apple Computer had to pay for the rights to The Beatles label Apple Music only when they entered the music industry (not that they didn't try to contest it!)
I think wary would have been a better word, but I really did mean "weary", as in I would find the ordeal tiresome or bothersome? I wouldn't disagree if you said that's bad grammar still.
Such a case would never end up in court. You can't sue someone for doing something that's perfectly legal.. well you can try, but it's going to be really hard to find a lawyer willing to waste their time (a lawyer you're going to have to pay).. and the case would ultimately get thrown out long before court.
Copyright is something different entirely!
https://xkcd.com/386/