To expand a bit on is guy's response.

The Chinese have not changed the pronunciation of the name of their capitol. However, Westerners have changed the way they represent the pronunciation (romanize) several times.

"Peking" comes one of the oldest systems of romanization called "Wade Giles." If you understand the conventions of the Wade Giles system and follow them, "Peking" is pronounced "bay-zhing." Unfortunately, if you do not know the conventions of the Wade Giles system you are almost guaranteed to mispronounce the word. Lots of Chinese terms became commonplace in the West with their Wade Giles romaniztions (e.g. Tao Te King). Unfortunately lots of Chinese terms continue to be systematically mispronounced because of the same romaniztion. In the "Tao Te King" example King is pronounced "jing." Of all the systems of romanization the Wade Giles is the most misleading.