I'm writing a paper on orthogonal polynomials and I have to cite results by Chebyshev and Cholesky. I found several and different transliterations from Russian. I wonder if there is a standard and accepted way to spell them. Thanks
Here you can hear the pronounce by a Russian speaking person.
As to the romanization, which usually does have a standard form in any language, I'd use the one of the language you are writing in your paper. In English it is Chebyshev (not Cheby_ch_ev). You can see the corresponding versions switching to other languages from the linked article in en.wikipedia (list of languages on the left).
Why not use the Cyrillic script? That is the canonical way of writing I would guess. (Leaving aside that Cholesky was French; his parents moved from Poland to France, according to wiki.)
All transcriptions are non-canonical, but equivalent up to (canonical?) isomorphism.
To quote wiki on Чебышёв:
Pafnuty Lvovich Chebyshev (Russian: Пафну́тий Льво́вич Чебышёв, IPA: [pɐf'n̪utʲɪ(j) 'lʲvovʲɪt͡ɕ t͡ɕɪbɨ'ʂof]) (May 16 [O.S. May 4] 1821 – December 8 [O.S. November 26] 1894) was a Russian mathematician. His name can be alternatively transliterated as Chebychev, Chebysheff, Chebyshov, Tchebychev or Tchebycheff, or Tschebyschev or Tschebyscheff (the latter two pairs are French and German transcriptions).
Finally, using non-roman script in LaTeX is not so hard anymore, these days.