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 like this idea. If you're a PS4 player you have a way around this problem (sort of). Go into your profile settings and change your display name, first and last, to whatever name you'd like to RP as. Sure, only friends and friends of friends can see your display name in place of your gamer tag, but that's good enough for me.