My last maiden name is Logan and I want to know if I am of Jewish descent. Logan was my grandmother's last name and she was from New York. I attend synangogue on Saturday having always been drawn to Judiasm.
There are Jews with last names that sound non Jewish and there are non Jews with last names that sound Jewish. A last name in itself would not prove whether one is a Jew or not. Jewishness is also determined via the mother, and it is possible that a Jewish lady married a non Jewish man by the last name of Logan, and now there is a Jewish Logan.
Per Wikipedia the name Logan seems to stem from Scotland. Most likely it is not Jewish, however it is always possible. Names were changed when people arrived in the USA. I would recommend that you discuss this with a competent Rabbi and a genalogist, who may be able to help you delve deeper into your past.