I sometimes get questions like "why do some restaurants serve "Szechuan" food, and some have "Sichuan" in their names? Which is correct? The answer is both.
In the same way, Nanjing is Nanking, Qingdao is Tsingtao (Beer), Beijing is Peking (Duck), and Chongqing is Chungking.
Wade-Giles Romanization and Pinyin
The latter names of these places are spelled in Wade-Giles Romanization, developed from a system produced by Thomas Francis Wade during the mid-19th century. However, this romanization system is outdated, and scholars criticize it for not representing Chinese phonetics well enough.
Pinyin or Hanyu Pinyin is the official romanization system for Standard Mandarin Chinese in China. Sichuan, Qingdao, and Beijing are spelled in Pinyin. If you plan to learn Mandarin Chinese, you will start by learning Pinyin. Pinyin means "spelled sounds." One of the reasons that the Chinese language is considered difficult is because it is written in Chinese form, and you have to memorize the pinyin (sound and pronunciation). Also, there are four tones. Words (in different writings) with the same spellings can mean different things without the tones.
Chinese Food Names
So some Chinese food are spelled in a different Romazination system, but some might be translated from other Chinese languages. See a few examples below.
Kung Pao Chicken 宫爆鸡丁
Kung¹-pao³ Chi¹-ting¹ Gōngbǎo jīdīng
Wade-Giles Mandarin Pinyin
Dim Sum 点心
dím sām diǎnxīn
Cantonese Yale Mandarin Pinyin
Chow Mein 炒面
It is the Americanization of the Chinese term chaomian.
Cantonese Mandarin Pinyin
wantan or wuntun húntun
Cantonese Mandarin Pinyin
Yes, Chinese dumplings have a Chinese name. It's jiăozi in Mandarin Pinyin.
Ok, it seems Chinese is complicated. Let's talk about the languages in China.
Mandarin and Cantonese
Mandarin or Putonghua, or Standard Mandarin, is the predominant language in China. Mandarin is based on the Beijing dialect. There are an estimated over 900 million Mandarin speakers (more than 60% of people in China) and over 80 million native Cantonese speakers in China (about 5% of China's population).
Hong Kong, Macau, and the majority of Guangdong province speak Cantonese, which is based on the Guangzhou dialect. Though Cantonese and Mandarin are written similarly, the spoken forms are different and not mutually intelligible. Cantonese favors traditional Chinese characters rather than simplified ones. See below.
Simplified Chinese Traditional Chinese
Dialects in China
As mentioned above, Mandarin is based on the Beijing dialect, and Cantonese is based on the Guangzhou dialect; the Chinese language consists of hundreds of varieties which are classified into several groups. Some of these groups comprise hundreds of distinct spoken forms － dialects. For example, I speak the Suzhou dialect growing up, which belongs to the Wu variety. Almost all of the lessons were taught in Mandarin in schools. Some of my teachers spoke the Suzhou dialect in their classes when I was in elementary school.
Proportions of first-language speakers [wikipedia]
Pinghua, others (0.6%)
There's much more to talk about how certain dishes get their names and how Chinese languages were developed. I don't want to overwhelm you here. If you have more questions, contact me and let me know.