北京

I speak occasionally with Australians who think that the Communist government changed the name from Pei King to Bei Jing when these are both different romanization of the same name. They think that the Communist Chinese government changed the name for the same propaganda reasons as the Vietnamese changing the name of Saigon to Ho Chi Minh city or The Soviets the name St Petersburg to Stalingrad. This shows little understanding for Chinese History. Here is a little excerpt from Wikipedia:

Peking is the name of the city according to Chinese Postal Map Romanization, and the traditional customary name for Beijing in English. The term originated with French missionaries four hundred years ago and corresponds to an older pronunciation predating a subsequent sound change in Mandarin from [kʲ] to [tɕ]^{[citation needed]}. ([tɕ] is represented in pinyin as j, as in Beijing), and is still used in some languages (as in Dutch, German, Hungarian, Polish and Spanish).

In China, the city has had many names. Between 1368 and 1405, and again from 1928 [1] and 1949, it was known as Beiping (北平; Pinyin: Beiping; Wade-Giles: Pei-p'ing), literally "Northern Peace". On both occasions, the name changed — with the removal of the element meaning "capital" (jing or king, 京) — to reflect the fact the national capital had changed to Nanjing, the first time under the Hongwu Emperor of the Ming Dynasty, and the second time with the Kuomintang (KMT) government of the Republic of China, so that Peking was no longer the capital of China.

The Communist Party of China reverted the name to Beijing (Peking) in 1949 again in part to emphasize that Beijing had returned to its role as China's capital. The government of the Republic of China on Taiwan has never formally recognized the name change, and during the 1950s and 1960s it was common in Taiwan for Beijing to be called Beiping to imply the illegitimacy of the PRC. Today, almost all of Taiwan, including the ROC government, uses Beijing, although some maps of China from Taiwan still use the old name along with pre-1949 political boundaries.