You don't have YOUR_LAST_NAME.com as a website, right? You probably don't have anything to worry about. Having a domain that does not have a business attached

You don't have YOUR_LAST_NAME.com as a website, right? You probably don't have anything to worry about. Having a domain that does not have a business attached means you're clearly not trying to do business on someone else's name. That takes away at least one of the 9 tests for trademark infringement.