Most of these people, I'm sure, had their real name on the account, or had their account linked to from some page with their real name, so Googling for their handle would easily find it.
At that point, as he mentioned, many of these people were college athletes, so their names would also show up on rosters and various campus newspaper accounts of games.
While it is possible to harass anonymously if you try, it's pretty likely that many of these people didn't even try; they just didn't think and said the first thing that came to mind that they knew would get a rise out of Curt Schilling.