If I gave a character an epithet, could they still fall under the “x reader” category?

I’m new to writing fanfic and have been starting out with some x reader one shots. It’s going well but I’m still figuring out the “rules” (if there are any) between something being x reader and something being an OC, besides giving the character a name. If I gave a character an epithet (for example “Fox Sin of Greed” Ban or “Surgeon of Death” Trafalger Law) would that be too specific to still consider it an X reader? Especially if backstory to explain it is given? Or should I just make it a full OC at that point? I guess I can write whatever I want but I know people complain about some X reader stories just being an OC without a name. Thanks!