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 think it's a great idea. It would be done better justice as a poll though so Bungie could see the percentages so they can see the number instead of reading each post. If u don't agree that's cool. Just as seeing as how this is a question for yay or nay you might wanna make a poll. ;o)