During a press panel at Wondercon, CINECHEW reports that Andrew Kreisberg was asked during the Q&A on the proper way to prounced the head of the leagues name.
Kreisberg said, "This is actually something that came up a lot when we were making the show. Before the nolan franchise, a lot of comic book fans pronounced it 'Raysh', but once Nolan started to pronounce it 'Rawz' - it changed everything. We wanted to please both the people who were fans of the comics and fans of just the films/shows. So we decided that members of the league would pronounce it 'Raysh' on the show, and non members would pronounce it 'Rawz'. "
Personally, I think we know there's only one way to say it which is 'Raysh', but I think this gives us a lot of insight to the confusion on why literally every character on the show pronounces it differently.
SOURCE: CINECHEW