Continuity mistake: At the end of the episode, Odo has sent everyone affected by the telepathic matrix to a cargo bay. Sisko and O'Brien remove their com badges, throwing them aside before heading to the bay. After everyone is cured, Sisko straightens back up and, in the closeup, you can see that he has a badge on. In the next closeup, it's gone again.
Continuity mistake: When Kira is explaining to Jadzia in Quark's that she wants to get rid of Sisko, she is wearing her Bajoran earring in her right ear. When she picks Quark up by his collar a couple of shots later, the earring is gone.
Chosen answer: No. He's given his name, that's all. Nothing there that might lead to a paradox. If he's gone into detail about his time travelling, that might cause an issue or two, but simply stating his name does nothing.
Tailkinker ★