TL;DR: from the name Khitan, a Mongolian tribe which once ruled Northern China; got to Russian from Mandarin via a Turkic language.

Китай: From Old East Slavic Китай ‎(Kitaй), from a Turkic source; compare Kazakh Қытай ‎(Qıtay), Kyrgyz Кытай ‎(Kıtay), Uzbek Xitoy, Turkmen Hytaý; from Old Turkic Qïtaǰ “Khitan”, from Mandarin 契丹 ‎(Qìdān, “Khitan”), the Chinese name of a Mongolian tribe who ruled Manchuria from 907–1115 CE.

Cognate with Spanish Catay and English Cathay.

Почему 中国 называют China ...

I wouldn't expect it to work, to be honest, while the meaning is the same, you're using words that are totally different.

Have you ever visited China? - accepted today 17/04/16