Ouch. You didn't mention that earlier.
The hospital sued you, had your last known address. Here's what might have happened. The process server went to the door. A male came to the door. "Are you D. Pool?" "Yes." "Here."
Bingo! Proper service.
I know. The whole same name situation didn't even factor into my mind until I started racking my brain, trying to understand how no one in the house told me this or gave me any relevant documents. The middle initial was never used on any of the paperwork.
I actually confirmed with my younger brother that he does remember someone coming to the door asking if [my name] lived there and if he knew me. That explains why the paperwork said "male occupant behind door." However, the paperwork also says that the occupant was 18 or older. My brother just turned 16 on the date of this encounter. My brother said he doesn't remember him asking for his age, but wouldn't have lied if he did. According to NYS, this may be considered bad service: "If the papers are left with a doorman, or a child, or a mentally disabled person, this is bad service."
He never told me because he assumed it was for my father. He didn't tell my father because he was and has been estranged from him.