I doubt Worf would be well known in the Empire outside those in the High Council. He is essentially an outcast and for most of his life from a shamed family. I can see most Klingons considering any stories of a one of them as part of Starfleet as an outrageous myth as well.
Even in "Sons of Mogh" a few adjustments was more than enough to fool the Klingons on the docked warship. In the end it wasn't his face that gave him away, but his body language, and you would think that if any Klingons who would be likely to know about who he is would be it would be those on a ship forced to dock on DS9.