I'm not sure either, what this thread has to do with Bible research ... but still, I guess is no more irrelevent than the Bible itself.
If the name refers to a certain dish that Wikipedia says is sold in North American Chinese restaurants, then the name should be pronounced something like 'swore,' but I think the S sound at the beginning needs more articulation (seperaton) to the 'wore' that follows.
The confusion arises because Chinese does not use an alphabet, so westerners need to transliterate the sounds into their own language. A number of systems have been used to to that, the original western system in English was called the Wade-Giles system.
The founding of the PRC in 1949 gave Chinese scholars the opportunity to develop their own system, commonly called 'Pinyin.' It is I think a superior system, and its used in China to (for example) to provide an alphabetical name for subway stations that westerners can read. It's in increasing use in western scholarly circles, except I think in the USA, where for ideological reasons, scholars need to demonstrate that they are not communists, by using the out-dated Wade-Giles system
Some sounds in Chinese need to be identified with two letters, as for example the combination ts, in this case.
If you refer to General Tso's chicken in Wikipedia, the author of the entry believes the General mentioned is a 19th century Qing General named in Pinyin, General Zuo Zong-tang. I would believe from my studies that Zuo is pronounced (as I said previously) 's-wore.'
And, of course the next problem is what tone should be used, but that's a whole different problem.