Red Wing was a famous boys' reformatory in Red Wing, Minnesota. Many of Dylan's early fans believed that Dylan himself had been incarcerated in Red Wing, but he never was. Further, there are many Minnesotans familiar with the place that doubt that Dylan ever laid eyes on it at all, as the school resembles a college much more than a prison, as he depicts it in the song.
Dylan performed this song live on occasion from 1963-1964, but it wasn't released until it appeared on the 1991 collection The Bootleg Series Volumes 1-3 (Rare & Unreleased) 1961-1991.
Who writes a song about a name they found in a phone book? That's just one of the everyday things these guys find to sing about. Anything in their field of vision or general scope of knowledge is fair game. If you cross paths with them, so are you.