Update: Late in the episode: Episode 455: Itachi's Story--Light and Darkness: Moonlit Night, Obito says something to Itachi that supports what I wrote below. It's basically an answer to this question in his own words.
Tobi: Within the organization, I'm known as Tobi. I'm not an official member. I'm a newbie within the Akatsuki who doesn't possess any spectacular jutsu. You should treat me as if that's true.
Itachi: Why hide your identity?
Tobi: If people knew Madara Uchiha was still alive, things would become complicated. Only the Akatsuki leader who we're meeting knows the truth.
The Tobi persona was actually very useful for keeping the heat off of him. Let's not forget that for most of the series, Pain was the acting leader of the Akatsuki. Obito was in the shadows, pulling Pain's strings. We can see this pay off, because he manages to avoid Jiraiya investigating him (he investigates Pain instead). And since he would rarely be around the Akatsuki, Obito was likely able to frustrate Itachi's efforts into looking into him (given Itachi never seems to have discerned he wasn't actually Madara). Itachi and Jiraiya are two people you definitely want to avoid sussing out your secrets, so I'd say staying in the shadows for so long was a really smart move.
I'll note, as said in another answer, Itachi was aware Tobi was Madara Uchiha. The Itachi light novels show him intuit this. Itachi actually comes dangerously close to guessing Tobi might be an Uchiha who went missing during the war (the truth), but in the end decides he must be Madara Uchiha. (see my answer here for quotes: https://anime.stackexchange.com/a/66266/19307)
Even after joining the Akatsuki as Tobi, Obito flies under everyone's radar because he acts like a total moron. Thus, he's still kept out of scrutiny and danger, as most people would rather try to investigate the leader Pain. But at the same time, the Tobi persona gives him the ability to monitor Akatsuki operations and members up close (such as Deidara).
Let us also remember what happens when Tobi reveals himself as Madara Uchiha to the kage. He's perceived as enough of a threat that the five great nations join together to try and crush him. That's how powerful the name Madara Uchiha is. If he'd revealed that too soon, before he was ready, all the Biju may have forever slipped out of his grasp. Obito has to carefully plan when and where to play this dangerous card, and he only goes public with it when he's reached his endgame. This isn't to say he never used this card before then; he revealed himself as Madara Uchiha to several individuals.