Stiglitz's celebrity has spread to the point where even a lowly soldier posted in France immediately recognizes him, stating that "everyone in the German army" knows him.
"Hey, who's that guy with Hugo?"
So, it's established that Stiglitz is well known in Germany and that the Nazis know he's running with the Basterds now. He isn't just a notorious serial killer; he's a serial killer who's still out there, killing officers, so it would be in the best interest of the Germans to remember his face. Especially if they're wearing a Gestapo uniform.
The Convenient Lapse in Logic:
Hugo Stiglitz is the most notorious member of the Basterds, so what do they do? They choose him for an undercover mission that absolutely depends on him not being recognized ... and he isn't.
The Basterds are recruited for a mission to infiltrate a film premiere attended by several high-ranking German officers, and Stiglitz is among those chosen to impersonate German officials, since he actually was one. Even if his face wasn't in the newspapers (it was), that's still a dumb plan, because all it takes is one person at the premiere who served alongside Stiglitz, was present during his incarceration or simply witnessed him scalping a fellow officer to ruin the entire carefully orchestrated plan.
It doesn't help that his name and theme song tend to magically appear anywhere he goes.