::::::LtPowers, given that "Jágr was the flag bearer of the 2010 Winter Olympics for the Czech Republic." (which why the hell is that not in the lede per WP:Worldview?) it is not "ridiculous" for a Czech to have a Czech name. We don't do the Ellis Island-type anglicization of BLP names on en.wp unless they change nationality. 
 ::::::As far as Moskva, please see English exonyms.