Names are supremely important in Judaism. The Creator's name ~ indicated by the Hebrew letters yud-hey-vav-hey in the Torah, the tetragrammaton ~ is so sacred we don't really know how to pronounce it at all. So, some say "Hashem" (the name) in its place or simply Adonai (Lord). Particularly observant Jews will often write G-d to express the deity, avoiding the whole word which is never to be defaced or erased. When Moses asks God who He is, God says cryptically, "Ehyeh asher ehyeh," which means something like "I will be what I will be."
In the Torah , the deity is referred to as El, Elohim, El Shaddai, even once as El Roi, The One Who Sees. In its attempt to connect with the divine, Judaism has assigned many other names to God, from the mystical to the practical. Some are functional or descriptive in nature, like Elyon, The Highest. Others are more conceptual or fanciful, like the Kabbalistic Ein Sof, The Infinite. Others, like Hamakom, The Place, take a bit of explaining. See below for more sources of information on the traditions of the names of God.
A very ancient expression of the divine name, Yah, is included in many Hebrew names, such as Eliyahu (Elijah) - My God (eli) is Yah - and Yirmiyahu (Jeremiah) - God will exalt.
So, many Hebrew names are biblical, for prophets or main characters in the Torah or other books... Daniel, Ruth, David, Hannah, Sarah, and so on. Others are to invoke certain qualities, like Meir (giver of light), or Ari (lion), or Binah (wisdom). Converts often take on Sarah or Abraham, after the matriarch/patriarch, or they pick names that have special meaning to them. Mine is Devorah bat Ezra, for the biblical woman I most admire, and the scribe who is credited with writing down the Torah.
If you would like to order a custom-designed, hand-cut illustration of a Hebrew name, click here. It makes a lovely gift for a bar mitzvah or bat mitzvah, baby naming or conversion to Judaism.
Note: This post doesn't attempt to cover all the interpretations, permutations, and traditions of Judaism's treatment of names. It isn't a scholarly or definitive religious explanation. It is to illustrate that the business of names in Judaism is ancient and very rich with meaning. You should consult your rabbi regarding Hebrew names. Normative Judaism does not recognize the term "Yahweh" as a name for the Creator.