Answer:
It builds suspense because some know and some don't. You want him to reveal but he waits. When Penelope doubts that is is actually Odysseus, she starts to test him to see if it is actually himself. He reveals himself to friends and family by seeing his trusted allies first. Then his maid sees the scar on his leg. He also shoots the arrow effortlessly through the rings and later he reveals the secret of the bed that confirms that it is him. "Here let me show you something else, a sign that I am he, that you can trust me, look: this old scar from the tusk wound that I got boar hunting on aparnassus...(Homer, 405)".