Personal names generally cannot be trademarked. You would most likely need to have a business or other use case of your last name in order to be granted a trademark.
TBH this scares me quite a bit since we have all the family’s emails tied to the domain, not only would it be a huge pain to lose it but also a security risk. Weve had the domain for 10yrs or more at this point…
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.