Could it be a variant of Shoshana or Susanna? I searched on stevemorse.org, restricting it to female, Jewish immigrants. Instead of the name IS Tzizinu, I selected SOUNDS LIKE. From the results, these sound like the closest names given by Jewish Russian immigrants, 3- and 2-syllables:
Schischana
Schoischano
Susanne
Susanna
Chaisina
Cjusine
Chouchana
Chijene
Chassine
Chisini
Sziszano
Scheisini
Scheicne
Chesne
Jesna
Czesna
Chouzin
Sisne
I agree with the suggestion upthread that if you can trace your ancestor names, you might find a grandmother or aunt or cousin with a similar-sounding name.