Goodness, Indian logic at work again.
Qin is a transliteration using the pinyin system, which is based on the Latin alphabet. Or are you telling me that you guys invented the Latin alphabet or used the Latin alphabet in the past? Even "Cin" is not an Indian transliteration but a Latin alphabet based transliteration. The Russians don't even use Cin, Cina or China, they call China Kitay, which is probably based on a Mongolian tribe Khitai that lived between China and Russia.
All transliterations of China, Cin, Cina, etc. are based on the original pronounciation of the Chinese word for the Qin kingdom that later became the Qin dynasty. What Indians in the past have done is transliterating the Chinese sound into Sanskrit since Indians didn't use Chinese script. Everyone has to somehow write a foreign name with its own writing system. I'm sure Shanghai or Beijing is also written in one of the many Brahmic and hundreds of other scripts worldwide but that doesn't means that India or anyone else but the Chinese gave their cities the name.