These answers suck.
While on the surface they make a good bit of sense and therefore I don't really knock the people that gave them, the answers them selves just do not stand up.
Keep in mind that this is an anime and so little things like common sense do not really get in the way of story telling. The real problem with this all starts with the question which is based in common sense, and thus can not win out against the needs of story telling.
I understand that player information was given out, if it was forget law suits, laughing coffin members would of been gunned down on the streets for what they did. GGO would never of happened. However, while following the common sense of things, everything after the end of SAO would of happened differently. I believe it was stated that 6000 people and change were still in SAO when it came to an end. Most of those people woke at the same time. That would of been major news.
Most of those people would not know how they were freed, only that one moment they were in the game and the next that after an announcement that the game was cleared they woke up. However those members of the assault team they would know. The doctors and nurses that cared for them would likely question folks as they were seen and checked over. " It was amazing! Kirito saved us!" or versions of that statement would of passed unfiltered in the first few days. If not from Doctors and Nurses, from player to player. Most of the SAO players were in hospitals when they woke, so it is natural to assume numbers of them were in the same places. The SAO members would of spoken to each other if not the staff.
Kirito was well known in the game if not by his name, at least as the black swordsmen. Trying to keep the media from discovering the story of how they escaped in reality would of been like trying to capture water in your hands. You get some of it, but most pours through. Maybe they never link Kirito to his RL id, but that would only of raised the legend of Kirito that much higher. The hero of SAO humbly keeps his identity a secret?
For ALO, they used the same model for Kirito in that game that they used for SAO for our benefit, so we as anime watchers knew him the moment he was on screen. Asuna looks very different in SAO II from her SAO character and while I never forget who she is, it is an attention grabbing difference I never fail to notice. So I could almost forgive Suguha for not knowing Kirito in ALO right away. Siding with the answers others gave. However I'm not willing to. He does look the same, no matter the reasons. Maybe she does not know for sure that is him, and maybe he never talked about what his character name was in SAO with her. However she never questions him about just how very much he looks like Kirigaya Kazuto. That is pure story telling over common sense.
By the time SAO II comes along and he enters GGO There should of been lines of folks whispering rumors of him being the same Kirito from SAO, hell their should of been dozens of would be fame seekers running names like KiritoSAO, KiritoR1, and many others trying to cash in on fame that was not theirs. If any thing the only reason Kirito should not gotten much notice in GGO it is because people would of assumed he was another faker cashing in on the name of the Hero of SAO.
The answer to this question, pure and short, is Story. The writer of the manga and anime needed him to, and wanted him to, have less fame and acclaim then he would of had if something like this happened in our world. They needed his own sister/cousin to be utterly clueless about who he was.