I'm playing on the PS4 and I've had this issue ever since I first played the beta, but for some reason while playing Destiny my in-game ID shows as my old PSN ID which had a forced change almost a year ago due to not falling into the accepted guidelines instead of my actual current ID.
So far, this only happens in Destiny and I can't seem to figure out why, or how to fix it.
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Having the same exact problem here.