As someone who’s ethnically Jewish but raised Christian, and wants to be Jewish, what would my name be?

My maternal grandmother is Jewish, she was born in Brooklyn to a family that spoke Yiddish. She married a Jewish man and had two kids. He was abusive, she moved out of state and got a divorce. She converted to Lutheranism sometime after she married her second husband, my paternal grandfather. My mom was raised going to church and I ultimately was raised going to church. It’s not like my grandmother’s Jewish upbringing/past was ever hidden or covered up. I was raised Christian but knew about my heritage and had many close friends who were Jewish. I’ve always, for as long as I can remember, have just felt so connected to my Jewishness, in a way that doesn’t exist on any level for Christianity. I’m confident I want to intentionally live my life as a Jew.

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I’ve heard the adage “once a Jew, always a Jew” but I don’t know how it works if my Grandma converted to Lutheranism and was heavily involved in her church. I do know that an apostate, and all female descendants, are considered Jewish. It’s just the naming thing that’s tricky.

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Her parents names are Sam and Emma. If I were to get a bat mitzvah, or any service that would require my ‘Hebrew name,’ what would my full name be?

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I love the name Leah Shoshana and want that to be my name. I just don’t know if that would be followed by bat Avraham v‘Sarah or bat Samuel v’Emma.