When a card's ability text refers to its own title, it is referring to itself only, and not to other copies (by title) of the card. In other words, if you put a Title card into play attached to an opponent’s Daenerys Targaryen, it will be returned to your hand at the end of the phase.
If the card enters play as a duplicate, that duplicate will be returned to your hand at the end of the phase. If the duplicate is no longer in play at that point, nothing will happen to the card that was already in play. A duplicate of a Title attachment is not itself an attachment, so it is never considered to be attached to Daenerys Targaryen.