After the player names a card, check if the card you chose has that name. If it doesn’t, but it’s a creature card, you may put it onto the battlefield. If you don’t want to put that card onto the battlefield, it’s not a creature card, or it does have the name the player said, it simply stays in that player’s library without ever being revealed. The player then shuffles their library, including that card.

A “creature card” is any card with the type creature, even if it has other types such as artifact, enchantment, or land. Older cards of type summon are also creature cards.

Once you’ve chosen a card during your search, you must clearly indicate which card you’ve chosen (preferably without showing the front of that card to the player!). Then the player names a card.

You may search for any card, not just a creature card. Of course, if you choose a noncreature card, you won’t be able to put it onto the battlefield no matter what card the player names.