The mayor in Stranger Things is Larry Kline, not Gordon. I’d say he just changes his name because of the events of Stranger Things (possibly part of a cover up?) the only problem with this is that his PhD, which dates to ‘79, says “Lawrence Gordon”.
Very frustrating, the only thing that makes the connection viable is the only thing that makes it questionable. Everything else lines up just fine.
Though, the mayor literally only appears in season 3, so it’s possible the Russians got him his position and in term set up his false identity in the process - which explains why he’s only in season 3 as when the Russians had to leave he would’ve most likely lost his position. Hawkins is in Indiana, so it’s not like it’d be a stretch that the Russians chose him, of all people