Can you cast a creature face-down using morph without revealing what it is?

Morph (CR 702.36) allows you to cast a card with the morph ability face-down by paying {3} instead of its normal mana cost. While face-down, the card is treated as a 2/2 colorless creature with no name, subtypes, abilities, or other characteristics — opponents do not get to see what card it actually is (CR 702.36b).

You are not required to reveal the card to your opponents while it remains face-down on the battlefield. However, you must keep the card in a way that allows a judge to verify it legally has morph (or megamorph) if asked (CR 702.36e). You must also reveal it if it leaves the battlefield face-down, so opponents can confirm it was a legal morph creature (CR 702.36f).

You may turn the creature face-up at any time you have priority by paying its morph cost (the cost printed after the morph keyword). This is a special action, not a spell or ability, so it cannot be responded to in the same way (CR 702.36d).

Concrete example: You cast Willbender face-down for {3}. It sits on the battlefield as a mysterious 2/2 with no abilities. Your opponent attacks; you pay {1}{U} to flip it face-up, revealing its ability to redirect a spell or ability targeting you. Your opponent had no way to know it was Willbender while it was face-down.

Key rules to remember: CR 702.36a–f govern morph. CR 707.8 covers the general rules for face-down objects and what information is hidden vs. what must be verifiable.