In Nora's timeline, Barry is not publicly known to be the Flash. This makes sense until you remember Thawne was known by his real name in 2049, while still having his Wells appearance. This means they would have to know that he was an impostor, and I don't think people knew about the multiverse in 2049, so that would mean he was the Harrison Wells the world had known back in 2000-2015.
Knowing that the Reverse-Flash killed Nora Allen and was also the Flash's archenemy, how could the general public not connect the dots, along with the fact that Barry Allen and Flash vanished at the same time, and realize Barry was the Flash? Barry's own daughter didn't even figure out what happened to Barry's parents until he told her himself. How was his identity not publicly known?