From doing internet searches:
The Jewish ethnicity, nationality, and religion are strongly interrelated, as Judaism is the traditional faith of the Jewish nation. Converts to Judaism, whose status as Jews within the Jewish ethnos is equal to those born into it, have been absorbed into the Jewish people throughout the millennia.
The total world Jewish population, however, is difficult to measure. In addition to issues with census methodology, there are halakhic disputes regarding who is a Jew and secular, political, and ancestral identification factors that may affect the figure considerably.
So even amongst the Jewish people themselves there is a disagreement as to the who is or can claim to be a "Jew".
I have read The Orthodox Jewish Church only allows those who's maternal line are Jewish to be members. Otherwise one is a "Convert" to Judaism.
Unless your mother has proof her ancestors were "Jewish" by documentation, family records or temple membership, having such names is not enough proof to make claims of Jewish race or ethnicity, in my opinion. Also if one claims an ethnicity of being Jewish there are several ethic divisions of same and one needs to identify which one.