The name 'Koschei' has never been used in the television series.
In "The Dark Path" (Virgin Missing Adventures novel) the Master has recently taken the alias "Koschei", a name the Second Doctor completely fails to recognise, as he has never heard it before. And by the end of the novel, he has stopped using the name "Koschei".
However, in "Divided Loyalties" (BBC Past Doctor Adventures novel), the Master used the name "Koschei" while at the Academy, before he and his friends took their new names (the Master, the Doctor, the War Chief, etc.). This could be his real name, a nickname, or an earlier alias (notice that multiple stories tell us the Doctor was called "Theta Sigma" at the Academy, but it's not his real name), although none of those explains why the Second Doctor wouldn't later recognize the name.
Later, in the novel "The Face of the Enemy" (BBC Past Doctor Adventures novel), set during the Third Doctor's era, the Master meets himself from another universe who calls himself "Koschei". This is of course compatible with either of the above novels.