A very simple etymological research (by Wikipedia ) on Texas:

1. http://en.wikipedia.org/wiki/Texas#Etymology
The name Texas, based on the Caddo word tejas meaning "friends" or "allies", was applied by the Spanish to the Caddo themselves and to the region of their settlement in East Texas.
2. Caddo language - Wikipedia, the free encyclopedia
Caddo is the only surviving Southern Caddoan language of the Caddo language family. It is spoken by the Caddo Nation of Oklahoma. Today, only 25 elderly speakers are estimated to remain, none of whom are monolingual Caddo speakers, making Caddo a critically endangered language.
Pronunciation of "tejas" in Caddo is not explained. Probably, "j" represents the IPA palatal approximant [j], so the English transliteration should be /teyas/. Source:
http://www.ahalenia.com/kiwat/caddo_alphabet.pdf - you can see, neither "J" nor "X" letter is used in Caddo latin alphabet, but there is "Y" letter pronounced as in English, which makes me think the "tejas" is the IPA spelling.

3. Texas - Wikipedia, la enciclopedia libre
Texas o Tejas (AFI: [ˈtɛk.səs] en inglés y [ˈtexas] en español) es un estado situado en la región Sur de Estados Unidos.
Conclusion:
Caddo "tejas" (pronounced /teyas/ in English?) -> Spanish "Tejas" or "Texas" (both pronounced /tekhas/ in English) -> English "Texas" (pronounced /teksas/).
The Russian version just follows the Spanish tradition.