What traits of manhood did Telemachus portray in "The Odyssey"?
First, when Athena comes to Ithaca disguised as Mentes, a friend of Odysseus. Telemachus graciously welcomes his father's friend, and feeds "him" well. Telemachus has learned what it is to be a good host in his society.
Telemachus also calls an assembly in Ithaca, the first since his father left twenty years ago. Telemachus encourages the people of Ithaca to rally behind him to get rid of the suitors who are taking advantage of his generosity and being overall bad guests. In this way, Telemachus is assuming the role of a man in his father's stead.
At Athena's encouraging (though she was still disguised), Telemachus embarks on a journey to learn more about his father's fate. He behaves as a man and a gracious guest when visitng neighboring kingdoms to learn what he can about Odysseus.