Why was Chairman Mao known by two names Mao Tse tung and Mao Zedong?

its not two names but two ways of pronouncing it. Of course, the name is properly written using Chinese symbols. So the question becomes, "how do you render the name using English letters?" One method was used for a long time, giving us "Mao Tse-tung" (Also "Peking" for the capital). This was abandoned in the 1970's because it didn't accurately portray the pronounciation of the names. A different method was then used giving us "Mao Zedong" (and "Beijing")