Other mistake: Shortly after Quark, Rom and Nog arrive on Earth in the 20th century, just after they are observed through the one-way glass by the Army officers, the Captain in the hat who enters the room with the man in the suit to interrogate the Ferengi is wearing his rank bars on his shirt collar horizontally, parallel to his collar. The two bars of an Army Captain's rank should be worn vertically.
Other mistake: As Kira is showing Ziyal the Federation rifle, the compartment underneath the rifle flips open unintentionally.
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 ★