He did know. All of the New Avengers knew. He lost his mask during the breakout at the Raft that brought the New Avengers together. Around the same time in Amazing Spider-Man Aunt May's house burned down, so he moved in to Stark Tower with MJ and Aunt May. Jarvis and Aunt May even had a relationship (given what we now know about Jarvis, we should all be glad that it has been erased). Skip forward a while, and after an assassin hired by the Kingpin accidentally got Aunt May instead of MJ, Peter - now a fugitive after switching sides - became desperate. Every avenue failed, even when Stark put $2m in Jarvis' name to pay for her medical bills. Then Mephisto approached him and MJ. Mephisto made them a deal - restoring Aunt May to life in return for their marriage. He erased it, leaving them with only a tiny part of their "souls" that remembered that they were supposed to be together. Now, one of the side effects of that is that now, nobody remembers who he is - even the people who already knew before he unmasked, including friends like Daredevil and his fellow Avengers. People do remember him unmasking on television but nobody can remember who it was under the mask.