The name we used didn't get mentioned. As I was growing up, my dad would occasionally make this for breakfast, and we called it cowboy toast. An internet search indicates we were not alone.
If this is the same food I think it is, we called it "Adam & Eve on a raft." This was Wisconsin ca. 1950s. But it had to be two eggs settled into a depression crushed into the toast, as opposed to an actual hole in the toast. Or are you talking about something else here? Either way, now you've got me thinking about that for breakfast tomorrow.  🙂