“ In Scripture, a person’s name identified them and stood for something specific. This is especially true of God. Naming carried special significance. It was a sign of authority and power. This is evident in the fact that God revealed His names to His people rather than allowing them to choose their names for Him.”
(Read it here: http://bible.org/article/names-god)
(1) Elohim: The plural form of EL, meaning “strong one.” It is used of false gods, but when used of the true God, it is a plural of majesty and intimates the trinity. It is especially used of God’s sovereignty, creative work, mighty work for Israel and in relation to His sovereignty (Isa. 54:5; Jer. 32:27; Gen. 1:1; Isa. 45:18; Deut. 5:23; 8:15; Ps. 68:7).
Compounds of El:
El Shaddai:“God Almighty.” The derivation is uncertain. Some think it stresses God’s loving supply and comfort; others His power as the Almighty one standing on a mountain and who corrects and chastens (Gen. 17:1; 28:3; 35:11; Ex. 6:1; Ps. 91:1, 2).
El Elyon: “The Most High God.” Stresses God’s strength, sovereignty, and supremacy (Gen. 14:19; Ps. 9:2; Dan. 7:18, 22, 25).
El Olam: “The Everlasting God.” Emphasizes God’s unchangeableness and is connected with His inexhaustibleness (Gen. 16:13).