If you are working out what Hebrew name you'll choose, take a look at what Rabbi Milder has to say.
Note that he sent this message out and invited congregants who don't have a Hebrew name to get one on Shabbat Shemot, Friday, January 20, 2017
What's Your Jewish Name?
It's not Frank, even if you can transliterate that into Hebrew letters.
Your Jewish name includes your Jewish parent's name, because it is an indication of how you acquired your Jewish identity. That's why Jews-by-choice get the parentage of Abraham and Sarah [Avraham v'Sarah], not their own parents' names, as their own parents are not Jews. Similarly, the child of one Jewish parent and one non-Jewish parent includes the Jewish parent's name in his/her own Jewish name. This is a name that has a ritual role, and is a Jewish identifier; hence, the focus on Jewish lineage. So, if Peter (Pesach) has a Jewish father named Paul (Shaul) and a non-Jewish mother named Mary, his Jewish name is Pesach ben Shaul. His Jewish name is not Pesach ben Shaul v'Mary.
Back to Frank. Jewish names are names derived from Jewish tradition. They generally have a Hebrew etymology. For that reason, Carol is not a Jewish name. It may be the name of a Jew, but Carol's Jewish name is a name drawn from our heritage, not from the heritage of other peoples.
Many of us have Yiddish names. Some rabbis prefer to translate Yiddish names into their Hebrew equivalents, while others (like me) view Yiddish names as part of our heritage. Zisl ben Motke v'Sheindel is a name that might have been used for centuries in Jewish ritual contexts, like Ketubot (wedding contracts) or Aliyot (being called to the Torah).
Over the course of time, the pronunciation of Jewish names sometimes becomes corrupted. It is always appropriate to reclaim the authentic pronunciation of the person for whom you were named, particularly if the way your great-aunt pronounced it makes no sense whatsoever.
I would like to help you record your authentic Hebrew name. Please be in touch!