Qin/Chin refers to the Qin Emperor who first united China into a nation over 2000 years ago (i.e. when China was ruled by a central authority in the Chinese capital). Before that, China was a "Civilization state" that preceded the Qin Emperor by many thousands of years.
So the English word for China is derived from this, yes. It was transferred through Sanskrit and then through Persian, and then the letter "a" was added to the end as is common in Latin-influenced languages such as English.
It is basically the English take on the name Qin/Chin.
Obviously, you have right to question the word "dominate" here(Even I feel the word "dominate" a bit exaggerated)....And you're among one of the Chinese members i respect.
So I honestly suggest you to read this link, it won't take you more than 20 minutes and provides lots of other insights, it is resourceful and detailed, please do read(I'm not sure whether it is reliable, but they have provided references in the link): http://hinduwisdom.info/India_and_China.htm