Two possibilities here I can think of: the stain is on the surface of the display, OR the stain is IN the display itself; IE water intrusion damage to the OLED panel. This has happened to some people here on this forum in the past, and can't be fixed short of replacing the whole display.
If that isn't your issue, and if your watch is relatively new, you might have had something like bathroom/kitchen cleaning spray splatter on your watch which then had some sort of reaction with the oleophobic coating of the display. The coat, which is pretty BS really since it wears off within weeks or a couple months at best, is just there to make the display feel slick and smooth when you touch it with your fingers (and to reduce fingerprint smudges). You can wipe it off without too much trouble using a piece of clean dry cloth.
The display glass or crystal (depending on your watch model) is chemically very stable and doesn't stain permanently under any sort of normal circumstances, short of maybe hydrofluoric acid (which is some incredibly nasty stuff so you probably don't keep any around you... )
So TL: DR - either you just need to rub more, or you have damage to your OLED panel. In which case you need your watch serviced to fix.