Peking or Beijing? My findings.

To cut a  long story short, the “Beijing” spelling is a result of the current pinyin system. In Chinese, the city name has always been 北京 since the establishment of the PRC, so there wasn’t a name change per se, instead, the change from Peking to Beijing was just for its English spelling. It was not necessarily to correct mistakes, rather, it was to adopt a different transcription system.

The Peking vs Beijing question can fall into the Chinese phonetic transcription scope, and this topic of phonetic transcription can be really complicated.

It involves three spelling systems: the Wade-Giles Romanization system, the Postal Spelling system (aka. Chinese postal romanization), and the Hanyu Pinyin system. They are all sophisticated systems, and pretty interesting as well because, like any literate Chinese, I have seen quite a few examples that I can relate to, and I even had a few aha moments while doing my little research.

Basically, I checked definitions and brief introductions in Wikipedia and other online resources, and found the following very helpful:

"Wade–Giles (/ˌweɪd ˈdʒaɪlz/), sometimes abbreviated Wade, is a romanization system for Mandarin Chinese. ...was the general system of transcription in the English-speaking world for most of the 20th century..." (From: https://en.wikipedia.org/wiki/Wade–Giles)
Common examples of Wade-Giles transcription include I-ching (《易经》), Tai-chi (太极), Kong Fu (功夫), etc.

"Postal romanization[1] was a system of transliterating Chinese place names developed by the Imperial Post Office in the early 1900s." Based on Wade-Giles, this system was developed to facilitate telegraphic transmission.
Among the common examples of postal romanization are Peking (北京), Tientsin（天津）, and Tsingtao (青岛).
Resources:
https://en.wikipedia.org/wiki/Chinese_postal_romanization
http://baike.baidu.com/view/580286.htm
https://en.wikipedia.org/wiki/Pinyin

"Pinyin, or Hanyu Pinyin, is the official phonetic system for transcribing the Mandarin pronunciations of Chinese characters into the Latin alphabet in mainland China, Taiwan,[1] and Singapore." Beijing is the current pinyin of 北京. (https://en.wikipedia.org/wiki/Pinyin)

Despite all the changes, some places or brands with historic value are allowed to keep their old spellings, such as Peking University, Peking Opera, Peking Man, and Peking Duck. But of course, if you use "Beijing" in those names, most likely people can still understand you.

Hello Sophie,

Thank you for your research and your writing. It is very thorough and enlightening. Just a few small mistakes. The first phrase I think is the best English version of what you were trying to say.

Bob