I see that everyone is taking the globally famous thing literally, as in everyone not only know who you are, but what you look like as well. Interesting.
While this may not apply directly to your character, one who is globally famous could be an anonymous hacker or terrorist that we've all heard of but have never seen. Imagine if someone hacked the FBI - we'd all know about them, but we wouldn't all know who precisely they were. "Did you hear about that guy Lulz?" "The guy who shut down the FBI's power system for 20 hours? That was so amazing!"
And now that I think about it, this could potentially work for your character as well. "Everybody knows he's a runner, but nobody knows what he looks like." "Yeah, I heard he got some Johnson to give him a house in the hills. UP FRONT." "That's nothing - I hear Renraku wants to hire this guy to do their negotiating for them, but they can't figure out what the guy looks like."