TLDR, I made a new bungie account, unlinked the old one, and used the new one to have a "name change" a couple of years back. For some reason, in mission or raid I show up as my current but, in social menu's or whispers with people I had added on the old account, I still show up as my old bungie id. I can't log back into the old bungie account due to me unlinking all of the past accounts linked to it.
New friends or people who didn't have me added back then, don't see me as my older user. Just people I had added through bungie before I changed it.
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This issue comes up when Bungie friends or in-game systems cache your old Bungie ID from before you changed it. Even if you've made a new Bungie account and updated your name, anyone who added you before the change may still see your old tag in social menus or whispers. This isn’t something you can fix entirely yourself unless Bungie updates how friend data is handled. For now, your best workaround is to have people remove and re-add you manually.