You are not required to correct opponent’s statements about hidden characteristics of face-down cards

If your opponent had gained information about a card’s characteristics such as its name (for example by you revealing it to them), but it currently is face-down, the card’s identity is not public information, but hidden information (from the Magic Tournament Rules):

Hidden information refers to the faces of cards and other objects at which the rules of the game and format do not allow you to look.

From this rule, the definition of hidden information is not specific to cards never shown to the opponent(s), but instead relates to their current status. As soon as you stop revealing your card to the opponent (of course assuming you’ve given them an opportunity to read the card), all information about characteristics of the card become hidden information again, simply because it is now information your opponent isn’t allowed to look at.

So if your opponent is asking specifically about a card name, as the question suggests, you are not required to point out which of your face-down cards has that name.

There are, however, circumstances that might be reason enough to be more lenient with a rules interpretation in such a case, such as this one brought up by Gendolkari in the comments:

I think the biggest issue […] is that both players know that there is only one way that the player should know the face-down permanent’s name; and that is that it was the card that was publicly returned from the graveyard. There’s a big difference between saying “is this a Deathmist Raptor?” in a situation where a random card had been manifested or played as a face-down morph; and saying “is this a Deathmist Raptor?” in the situation described. Even though the words are the same, the context makes a big difference. In other words, in the context described, asking “is this a Deathmist Raptor?” is simply a clear shorthand for “Is this the Deathmist Raptor that you returned from your graveyard?”

(For a case in which they ask about the origins of the card instead, see murgatroid99’s answer.)

That said, you are allowed to correct your opponent about such information at your own discretion:

However, players may choose to reveal their hands or any other hidden information available to them, (…).

This is entirely up to you, though. You may be tempted to do so for example out of sportsmanship, or if you feel one of your actions (such as a switch in marker colors they glanced over in the heat of a match) had caused their misinterpretation of the situation – yet you’re never required to do so.