As detailed in an earlier post, Russian hypocoristics (pet names) comprise a rich onomastic lode, perhaps unparalleled in the world’s languages. When they are transliterated into English (or other languages using the Roman alphabet) their status as affectives is not necessarily recognizable as such by those who have no knowledge of Russian.
In this respect, the incidence of diminutives as first names among well-known Russian-Jewish violinists and pianists of the twentieth century born in the Pale of Settlement (Odessa, in particular) is to be explained by the fact that these were child prodigies who simply continued to use the hypocoristic form of their Russian forenames into adulthood as stage names. Thus the famous violinists Jascha Heifetz (R Иосиф Рувимович Хейфец), Mischa Elman (R Михаил Саулович Эльман), and Tossy(a) Spivakovsky (Натан Давидович Спиваковский) had the given (official) forenames Joseph (not Jacob, curiously enough, from which Jascha is the proper derivative), Michael, and Nathan, resp.; and the full forename of the pianist Shura Cherkassky (R Александр Исаакович Черкасский) was Alexander (Шура < Сашура < Саша < Саня < Алкесандр).
This early twentieth-century custom among Russian-Jewish child prodigies of keeping their pet names is understandable, given the desirability of maintaining reputations first won in childhood. In the event, for audiences and a general public outside the Russophone milieu the hypocoristic force is lost, and with time, even for a Russian speaker, the fact of a familiar performer well on in years appearing under a diminutive as a first name ceases to be onomastically dissonant.
[Addendum: One thing I neglected to mention (but can be inferred from what I did say) is that the older practice of keeping a pet name as a stage name fell into desuetude sometime between the wars. Odessa didn’t stop producing Wunderkinder (cf. David Oistrakh), but musical prodigies who post-dated the Mischas and Jaschas of yesteryear did stop following the older practice. – M. S.]