From looking at the Jewish Given names data bases in Jewish Gen and Ancestry for several countries such as Russia, Poland and Ukraine , the most common  male Hebrew names for Muni/Manya/Moni/Munke Mendl came out as 
Emanual , Menachem , Mordechai and Asher .  I could find only Marina as a female variant of Manya but no Yiddish or Hebrew derivation. . 

if Manya is a common nickname in Slavic countries  for Maria or Marina  , it might make sense that a Jewish woman might be given a non-Jewish local name like my friend , the singer Masha Benya , who was born at the beginning of the 20th century in Lithuania .  They might have been named after a relative named Miriam , Mirl or even Malka.  
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Henry H. Carrey