Names are more than just convenient labels; using your Jewish name is a proud proclamation of your Jewish heritage. The Jews of ancient Egypt, our sages tell us, cherished the tradition of using Jewish names. This was one of the ways they clung to their people and were deemed worthy of redemption.
Furthermore, the Jewish name is the channel through which they receive divine energy. In fact, when parents give their child a name, it is considered a small prophecy, since, in a way, that was the only name that person could have.
A girl receives her name during a Torah reading in the synagogue. Linking both events, the Torah reading and the giving of a name, bestows a blessing upon the name.
A boy receives his name during circumcision, when he enters into the covenant of Abraham.
If you don't have a Jewish name, you can choose one. People generally choose a name similar to their non-Jewish name.