If the Roman patrician was not especially poor for his rank he could probably have his slave body guards beat up the person who dared to question his rank.
As for inheriting a villa he had never been to, I suppose thaw there were at least a few legal formalities to inheriting property: he might be able to show a copy of the inventory of his father's estate including the villa as one property he had owned, for example, and a copy of his father's will, and maybe a receipt for paying inheritance tax on the villa, etc.
And when the parents died it would have been the duty of the estate manager to write to the heir and ask for instructions. And part of the plans they made could have been to have someone who knew the heir and was well known to the locals - maybe having visited the parents at the villa - go with the heir to the estate and assure the locals the heir was genuine.
Considering that during the Empire many wealthy persons owned properties in several different provinces separated by hundreds or thousands of miles, and even villas in Italy could be separated by hundreds of miles, no doubt there were procedures that were often used with some success to avoid the type of problems you imagine.
It would cost a lot of money to travel in the style of a rich Roman so if someone showed up travelling in the style of a rich Roman he would almost certainly not be some type of impostor.