It is customary to give a Jewish child a Hebrew name in addition to his or her English name. The Hebrew name is how the child will be known in the Jewish community when he or she is called up to the Torah, and gets married.
Traditionally, it’s considered very important to choose the right name for a child–a name has great influence on the development of that child’s character. There are no rules to guide parents in the naming of their children, but there are some prevalent customs accepted by Jews in different localities.
In America, most Jews are descended from Ashkenazic immigrants, and have generally followed the East European custom of making some connection between the two names given to a child at birth. The link can be phonic (English name Samara, Hebrew name Sarah) or taken from the meaning (English name Theodora, which means gift in Greek, Hebrew name Netanya, which means gift of God in Hebrew).
Because a name is so important to the overall identity and ideals of a child, many Jewish parents aim to select names for their kids that will strengthen ties to family or reinforce the historical continuity of the Jewish people. Hebrew names might not actually be Hebrew–some people choose Yiddish names as their Hebrew names, a tradition that goes back to Eastern Europe.