In issue 5 of Fraction's Hawkeye, it is revealed that Kate Bishop was posing as Madame Masque from the time Clint was grabbed to after the auction. How did she pull this off or even know where Clint was going? It is never explained or referenced.
She probably tailed Clint.
Look at the girl Clint stole the taxi from. Then look at the wig and glasses on Kate's mannequin head when she reappeared with Madame Masque bound and gagged. That answer your question?
Avengers 64 the team, not just the reader, finds out Clint's name for the first time. Did no one ever bother to ask him at any point what his name was? He had a relationship with Black Widow, why did she never ask? It seems like a strange thing to have never come up.
Meta reason: The writers hadn't thought of it or deemed it necessary. Particularly in the 1960's, villains (remember that Hawkeye started off as one) didn't often get real names (see also the Vulture from Spider-Man). In-universe reason: Clint was often hot-headed in the early days of joining the Avengers, so its quite possible that the others merely tolerated him and didn't want to spend time with him that much - thus explaining why they wouldn't know his real name. Add in the fact that his brother was a supposedly notorious criminal at the time, and it's quite plausible that Clint would have dodged any questions about his real name, not wanting to be be associated with a criminal when he was just starting to reform himself. As for the Black Widow, I don't recall her saying that she didn't know his name in that issue - it's possible that he could have told her off-panel.