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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It's probably not going to happen [quote]Why can't we name our Guardians? Will that option be available in the full game or are we stuck with our Gamertags/IDs? The team thought a lot about how best to have players identify themselves in the world. Ultimately, we’ve landed on PSN ID and Xbox LIVE Gamertag, so other people don’t have to manage a third list of identities (real name, platform tag, Destiny character name).[/quote] [url=http://example.com]http://m.ign.com/articles/2014/07/29/bungie-answers-your-destiny-questions-ign-first[/url]