We've all made our guardians just how we want them; they're the class we want them, the race we want them, and they have the face we want them to have. It'd be a subtle, yet great customisation option if we could name them.
It shouldn't show as a display name though, it should only be visible to others when they inspect your character.
EDIT: to support and sign the petition, leave a comment saying: "Name our Guardians"
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I have suggested the same thing. I feel it would be a wonderful addition to the game. Keep are PSN or XBL account names private & give us the chance to give all of our characters unique, individual names.