What does Monte Cristo ask Haydee not to tell in The Count of Monte Cristo?

The Count asks Haydee not to tell anyone about her parentage if she chooses to leave him.
Although he introduces her to society as his slave, the Count is more than happy to allow Haydee to live her own life. But the Count still loves her and feels incredibly protective towards her all the same. That's why he doesn't want her to reveal to another living soul the identity of her father, the Ali Pasha. Otherwise, he's worried that she might get mixed up in the imminent scandal that he knows is about to break concerning the disreputable behavior of Fernand. The Count is determined to destroy the man who helped send him to prison on a trumped-up charge and he doesn't want Haydee to get caught up in the crossfire.