The airport was named "Howard R. Hughes Airport" from 1938 to 1940; Hughes was responsible for several improvements to the airport, including its first control tower, built in 1938. The airport's name was changed back to Houston Municipal because Hughes was alive at the time and regulations did not allow federal improvement funds to an airport named after a living person. The 1940 terminal building (now a museum) shows "Houston Municipal Airport", so the change was probably made by 1940. I have no idea what the mission was that was transferred to Sweetwater, but Houston Municipal did hold WASP classes in 1943. Houston Municipal became Houston International in 1954 and William P. Hobby Airport in 1967.