There are many customs about how and what to name your child.
Yes. According to Jewish custom, every Jewish child is given a Jewish name at his bris. This name is used for many purposes including being called up to the Torah and many other Jewish rituals including marriage and divorce.
The Talmud teaches us that in the merit that the Jewish People kept their Jewish names, they were redeemed from enslavement in Egypt. A Jewish name is a display of pride to be part of the Chosen Nation.
In Many Ashkenazik communities the custom is that the mother chooses the name of the first child.
Traditional Jewish Names:
Boy: Avraham, Yitzchok, Yakov, Yosef, Reuven, Shimon, Levi, Yehudah, Yessachar, Moshe, Aron, Chaim, Shmuel, Eliyahu
Girl: Sarah, Rivka, Rochel, Leah, Yehudis, Chava, Tziporah, Avigayil
Modern Jewish Names:
Boy: Abraham, Issac, Jacob, Joseph
Girl: Sarah, Rebeca, Rachel, Brenda