I missed where he explicitly made a claim about it one way or the other.

The months went by, and at last on a day of spring Ged returned to the Great House, and he had no idea what would be asked of him next. At the door that gives on the path across the fields to Roke Knoll an old man met him, waiting for him in the doorway. At first Ged did not know him, and then putting his mind to it recalled him as the one who had let him into the School on the day of his coming, five years ago.

The old man smiled, greeting him by name, and asked, "Do you know who I am?"

Now Ged had thought before of how it was always said, the Nine Masters of Roke, although he knew only eight: Windkey, Hand, Herbal, Chanter, Changer, Summoner, Namer, Patterner. It seemed that people spoke of the Archmage as the ninth. Yet when a new Archmage was chosen, nine Masters met to choose him.

"I think you are the Master Doorkeeper," said Ged.

"I am. Ged, you won entrance to Roke by saying your name. Now you may win your freedom of it by saying mine." So said the old man smiling, and waited. Ged stood dumb.

He knew a thousand ways and crafts and means for finding out names of things and of men, of course; such craft was a part of everything he had learned at Roke, for without it there could be little useful magic done. But to find out the name of a Mage and Master was another matter. A mage's name is better hidden than a herring in the sea, better guarded than a dragon's den. A prying charm will be met with a stronger charm, subtle devices will fail, devious inquiries will be deviously thwarted, and force will be turned ruinously back upon itself.

"You keep a narrow door, Master," said Ged at last. "I must sit out in the fields here, I think, and fast till I grow thin enough to slip through"

"As long as you like," said the Doorkeeper, smiling.

So Ged went off a little way and sat down under an alder on the banks of the Thwilburn, letting his otak run down to play in the stream and hunt the muddy banks for creekcrabs. The sun went down, late and bright, for spring was well along. Lights of lantern and werelight gleamed in the windows of the Great House, and down the hill the streets of Thwil town filled with darkness. Owls hooted over the roofs and bats flitted in the dusk air above the stream, and still Ged sat thinking how he might, by force, ruse, or sorcery, learn the Doorkeeper's name. The more he pondered the less he saw, among all the arts of witchcraft he had learned in these five years on Roke, any one that would serve to wrest such a secret from such a mage.

He lay down in the field and slept under the stars, with the otak nestling in his pocket. After the sun was up he went, still fasting, to the door of the House and knocked. The Doorkeeper opened.

"Master," said Ged, "I cannot take your name from you, not being strong enough, and I cannot trick your name from you, not being wise enough. So I am content to stay here, and learn or serve, whatever you will: unless by chance you will answer a question I have."

"Ask it."

"What is your name?"

The Doorkeeper smiled, and said his name: and Ged, repeating it, entered for the last time into that House.

--A Wizard of Earthsea Ursula K. LeGuin

http://tvtropes.org/pmwiki/pmwiki.php/Main/YouDidntAsk