Also the date in JL #15 happened in Boston, maybe they're used to seeing Wonder Woman - why would you assume it was Wonder Woman in the club in London.
Isn't that why Celebs get out of their usual environments, and why many choose London!
And that's even with the signature jewelry - available I'm sure for cosplaying - for example, just suppose you saw a elderly lady in a Boston Cafe that looked like the Queen of England having a cup of tea would you think it was the Queen, or just someone look-a-likey? What makes the Queen - the Queen, is the hoopla that goes with being Queen. Driving a Landrover in a headscarf she looks like any other country type of old lady that drives old landrovers around and about.
Or if you were an ace-reporter like Lois Lane who is so totally awesome who happened to see Supergirl - in full costume - at Clark Kent's apartment, you don't assume this is *the* Supergirl, but a cosplay.