Can a rental property owner be served a subpoena for a person claiming the property as residence?

Serving you would not be valid service.

The only way that it possibly COULD... would be if you and this other person were both adults living in the same household.... which isn't the case.

The process server just wants to get paid.... tell them they have the wrong address and to leave you alone.

Not sure what your asking. If the subpoena is in your name you have to respond to it. You can call and explain you don't know the person but they still may make you appear. If the subpoena is for the other person, but delivered to your property you can call and tell them they don't live there, but you are under no obligation to do so.

It's not your job to find the person named, so you simply refuse service for anybody who isn't there. If you're not a party or a witness then it's unlikely you'd be subpoenaed.

Are you person named on the subpoena? If so you must respond to it. If you are not, don't worry about it.

no, a subpoena must be served personally to the individual, don't worry about it.