Also keep in mind that he is a king, which means he's from a noble family and probably is used to getting his way. He is known for being clever and playing tricks, such as the Trojan horse. He is loyal to his men and other Greek leaders, and he tries to be faithful to his wife. I think the movie Troy portrays him very well, but my favorite Odysseus/Ulysses is Kirk Douglas in an old movie. I think the title is Ulysses.
I'm not exactly sure what is meant by his total identity, but here goes . . .
Odysseus is described as being not quite a god, but not a mere human. He had the support of the gods throughout his journey to Troy for the Trojan war and all the way back home from Troy to Ithaca to rejoin his family. Because of his kind of elevated status among his men, he was very conceited. He was obviously handsome or desirable to the gods because Athena loved him more than any mortal and her favor is what drove Zeus to order Calypso to let him go (another most beautiful goddess who kept Odysseus "prisoner" as her lover for seven years on her paradise island). He blames the gods when things go wrong and praises himself when they go right. He is extremely loyal at heart to his wife and son, even though unfaithful physically, but that probably has much to do with the view of women in ancient Greece. He is careful and thoughtful, when he arrives home he doesn't just barge in but disguises himself (or rather Athena disguises him) so he can assess the situation at home. He is a good leader and managed, with the help of the gods, to defeat the Trojan army with the Trojan horse trick. Odysseus' total identity entails many facets, but I hope this helped get you on the right track.