I haven't seen this in Lithuania, but in German-speaking areas in the
19th century Marx was very commonly a civil name used by men whose
Hebrew name was Mordecai. I wouldn't call it a "shortened" form,
although it's certainly shorter when written in English; it's more
along the lines of the frequent associations of Philip/Feivel or
Emanuel/Menachem. Why would someone from Lithuania use "Marx" as their
civil name, rather than Marcus or Mark (or Mordecai, for that matter)?
You'd have to look at when and where he adopted that civil name, and
you haven't told us anything about that. Even in Lithuania, I think
German might have been used as a cultural step up, rather than
Russian: it was the language of a neighboring country with more
enlightened policies than Russia's, and it was easy to learn for
someone whose native language was Yiddish. But that's just a guess.

Dick Plotz
Providence RI USA