What are the names for God that are used in the Hebrew Bible?
There are many different names for God in the Hebrew Bible, or the Tanach. These include YHVH, Adonai, El, Elohim, El Shaddai. In addition, God is called by many epithets - YHVH Tzvaot (Lord of Hosts), Tzur (Rock), etc. The epithets reflect the different ways we relate to and think of God in different times and in different situations. The various names of God probably also reflect this, but historically also probably reflect an assimilation or adoption of various Canaanite and other cultic gods into the persona of the Israelite God.
Etymologically, the meanings and origins of the names of God are a complex and difficult subject. The standard scholarly dictionary for Biblical studies, A Hebrew and English Lexicon of the Old Testament, by Brown, Driver and Briggs, assumes that Elah is the root of El, possibly of Elohim, but writes that perhaps El and Elohim come from different roots, El coming from a root meaning 'strong', and Elohim from a root meaning 'be in front of', so that El is God the Strong One, whereas Elohim is God the leader (the one who goes in front). But theories vary. Perhaps Elohim comes from Eloha and has the root meaning of 'fear'. YHVH seems to come from the root HVH - 'to be' - and has the meaning 'the one who is', but again, this is a matter of some speculation.