Question

How do we know Telemachus recognized Athena?

Answer 1

Telemachus visited Nestor with Athena while in disguise as a mentor. She later turned into a bird and flew right in front of him, right then he knew that he was in the company of a God.

Answer 2

When Telemachus was visiting Nestor with Athena in the disguise of Mentor, after a while She turned into a bird and flew away, right in front of Telemachus. At that point Telemachus knew that he had been in the company of a God. So i believe that Homer tells us in the narrative.