The word 'Koschei' has never been said in television Doctor Who.
There is no character whose actual name is 'Koschei' in the spin-offs either. However, in the Virgin Missing Adventure novel The Dark Path, the Master uses the alias 'Koschei'. This is no different to his use of other aliases such as 'Emil Keller'("The Mind of Evil"), 'Kalid'("Time-Flight") or 'Harold Saxon'("The Sound of Drums"/"Last of the Time Lords").
So in short, 'Koschei' is the Master, or more accurately, one of his various temporary aliases.