I have some comments on the spelling in Polish.
There could be three consistent initial clusters:
Polish "Sy-" is similar to the English "see". A hard "s".
Polish "Szy-" is similar to the English "she". A hard "sh".
Polish "Si-" is also similar to the English "she" but very very soft.
Thus, the spellings "Szi-", "Shi-", etc. are inconsistent in Polish.
Please note that in Polish, there is not a soft "s" but a soft "sh" instead. In Russian, there are both hard and soft "s" and only a hard "sh".
Thus, "Syma" could be just the Polish spelling of the Russian name "Sima". Sima can be the nn of
Serafima, as supposed by Lassia.