You have a number of things to worry about:
Will there be competition for things like website domain names, social media handles, etc.?
Are you violating any trademarks?
Will these other people try to attack you legally? (Even if they have no basis in law, that doesn't stop them from threatening you; that can get expensive if you have to get your own lawyers, and can cause sleepless nights.)
Will Apple notice and complain?
What will happen when people search (Google / App Store) for this app name?
Your example is a bit difficult to follow, because you say your name is "unusual ... just made up", but then you give the example "Car", which is not a made-up word at all. Contrast: Apple is not a made-up or unusual word; Tgweoxy is a made-up word.