I'm working on my Black Legion and I had the idea to add a bit of a personal touch on the army since fluffwise it would have been an independent warband before "taking the Black". I seem to recall, although I can't remember if it was explicitly stated, that you essentially give up your previous identity when you join the Black Legion ("Brotherhood for the brotherless", "children of failed fathers" and all that). It's been a while since I read Talon of Horus and Black Legion (might be time for a re-read) but while I know there's still minor subgroups in the Legion (Telemachon's "Shrieking Masquerade", Falkus' "Aphotic Blade", Lheor's "War God's Maw" etc.) I can't recall if there's anything unique about their armor style (although IIRC Telemachon's group are Slaaneshi Raptors/Warp Talons or both and Lheor's are Khorne Berserkers), like an additional splash of color or something on the otherwise black armor.
Without getting into "my dudes", is there official lore saying one way or the other? I'm still debating if I wanted to do it or not but I had the idea of adding an extra color, like an arm or shoulderpad or something in a non black&gold color to identify the specific warband's allegiance within the Legion, I just can't remember if that's actually a canon thing.