Anakin, ALL the cool Sith are doing it!
I can totally see why Senator Palpatine might need a nickname. I mean as slow and stunted as the Jedi were in TPM, you would think that if a DARTH Sidious was nominated for Chancellor they would put two and two together and realize: 'Wait just one second Mister! Darth? Isn't that what comes before ALL Sith names? And doesn't it seem strange that he was smiling when Queen Amidala decided to go back to Naboo??? He must be a Sith Lord! Get him!!!'
But why does Anakin need one?
Way I see it...in Ep III Anakin will turn to the darkside, and will go by the name of Darth Vader while doing Darth Sidious' dirty work.
BUT...as the Jedi mount one last ditch effort to overthrow him, Ani comes running claiming to have seen Emperor Palpatine for what he REALLY is! A LAWYER!!! And a Sith Lord. And Ani will convince them that he wants to join them in their attempt to overthrow Emperor Palpatine.
You see...as far as the Jedi know, Anakin is just Anakin, they don't know that Anakin IS Darth Vader. As far as the Jedi know this Darth Vader they've been hearing about is just ANOTHER of Sidious' apprentices...Darth Maul, Darth Tyranus, Darth Vader, what else is new?
Ofcourse Ani IS Darth Vader and he leads the Jedi into a trap and they're totally SCR@WED.
Right afterthat , BTW, is when I think the Obi-Wan/Anakin duel occurs.