The curse of the Cowl is to hide the name of its wearer. You break the curse by revealing the name.
And so infallible are the Elder Scrolls, and so strong was the curse on the Cowl that breaking the curse actually altered time... retroactively. Dareloth's house became a new Guild Hall without you even having to lift a finger.
I suppose it could be argued there was a minor Dragon Break right there, and the Jills mended history. Because the curse could never have been broken, was broken by an object of even greater power, they fixed history so that the person retained their identity, but became the Gray Fox when the Cowl was off.
Bleh, I'm going to make [censored] up and say the guards and lords put a strict gag on any mention of the TG in Cyrodiil. Hey, the capital country needs to look its most pretty. Else where, it's much more loose. Well, that's my logical input on why the TG is hush hush in Oblivion.
It could be that the Thieves Guild being a heck of a lot more undercover in Cyrodiil is because it's the Empire's strongest area. Back when the Empire was at the absolute height of it's power, the Thieves Guild was stamped out in Cyrodiil and was similar to what they are now in Cyrodiil in other provinces. But now that the Empire's decreasing, like a tide, the Guild moves back in, slowly consolidating their power until they feel free being a little more open.