‎أحسن الله إليك Is it permissible to wear a watch that has the name from greek mythology origins, or shoes? I mean just the name, no logo. Or is it better to stay away due to its origins?

If it really has a name that glorifies a Greek god or so, then of course you should stay away from it. However, it must really be the case and not just mere speculation or doubt. Either way, the best thing to do is to stay away from such brands and get something that doesn't have a shubha (suspicion) in it, so that you don't worry about these things.