Did you notice that the knights in Le Morte D'Arthur are often running around in disguise? Many knights, like Gareth, Trystram, or Launcelot, choose to withhold their identity in order to be judged solely on the basis of their fighting skills and honorable behavior. Others, like King Mark or Sir Palomides, conceal their identity out of fear, envy, or a desire to deceive.
Whatever his reasons for going incognito, the knight usually only reveals his identity after his character is fully formed, like after he has defeated the best knight in a joust, claimed a wife for himself, or made a powerful friend. And as soon as a knight reveals himself, he also reveals his family ties, which tells everyone pretty much all they need to know: how he's connected to the king.
In Arthur's case, the slow revelation of his family ties solidifies his identity and his right to rule the kingdom, revealing just how important this aspect of a person's identity is to his character. Yet some characters, like Gareth, choose to disavow family ties as a means of disavowing what their family represents – in Gareth's case, blood vengeance. By defining himself against his family by associating with its enemies, like Launcelot and Trystram, Gareth chooses an identity that goes beyond them.
Knights in Le Morte D'Arthur choose to conceal their identities in order to be judged on the basis of their deeds alone.
You can tell a lot about a man from his friends, and who a knight chooses to associate with in Le Morte D'Arthur reveals as much about his identity as anything he does.