Names held a very important place in the Biblical Revelation. A person's name was the Revelation of his character. He was as his name described. That is why when a person's character changed in the Bible their name also changed. 2 Kings 23:34; 24:17; 1 Samuel 25:25 Abram - Abraham, Genesis 17:5 Jacob - Israel, Genesis 35:10 Saul - Paul Acts 13:9 etc. This use of names becomes meaningful when the names of God are examined. The different names of God reveal something about God's character or actions. Often they sum up the meaning of given period of God's History. These names are not names that man has given to God but rather names given by God to Himself. Sometimes God's attributes are added to his name to reveal God's character as in 'the Holy One of Israel.'

The Lord is One
One of the great mistakes about the Bible is to think that God has revealed himself in the Old Testament as Father and that in the New Testament he has added two other persons to the Godhead. How can the God of love of the New Testament be found in those violent parts of the Old Testament?
For Further Study See Background to Joshua in The Scroll

However the Bible itself makes it clear that the God of the Old Testament and New Testament are one God. This was the cry of the people of God in the Old Testament. The Shema declared the unity and oneness of God. Deuteronomy 6:4-9; Mark 12:29-32 Then the Trinity, Father, Son and Holy Spirit, is gradually revealed throughout the Scriptures until they come into full expression in the New Testament. God has not changed, rather he has been gradually revealed. Deuteronomy 32:39; Isaiah 43:10; 1 Corinthians 8:4; 1 Timothy 2:5

Yahweh
Although this is the Mosaic name for God it is generally used for God throughout the Old Testament. In Hebrew the name is spelt with four Hebrew consonants, which in English would look like this YHWH. When vowels are put to it then it looks like this 'Yahweh'. Sometimes it was translated by Jehovah. This is a personal name and not a noun meaning 'God'. In the New Testament the Hebrew word Yahweh is used for all three persons of the Trinity. 
 

Person	New Testament	Old Testament
Father	Hebrews 12:5,6	Psalm 94:12; 119:75
Son	John 12:41	Isaiah 6
Holy Spirit	Acts 28:25	Isaiah 6

The three persons of the Trinity in the New Testament is the Yahweh of the Old Testament. 

The Hebrew had such a reverence for God that he would never dare say the name of Yahweh . In place of the word Yahweh he would substitute the name of 'Lord'. Many translations of the Bible have kept this practice and have used LORD all in capital letters to refer to God as Yahweh.

It was Moses who first received this Revelation of who God is. Although the name had been used throughout Genesis, its true meaning had never been explained for Israel. Exodus 6:2,3 The Hebrew people knew the name as a sound but didn't know what it meant. It was an abiding Revelation of who God is and it was also a form of the Hebrew verb 'to be'. Exodus 3:13-15

The Hebrew verb 'to be' is the key to the meaning of Yahweh. But the word means more than just the fact that God exists. It speaks of God' self-existence, self-sufficiency and eternity but it also carries the meaning of 'to be or become a present reality'. It has the idea of God being our Redeemer. In Exodus 3:14 when God reveals himself as 'I am that I am', God was telling Moses more than the fact that God existed or even pre-existed. God was telling Moses that He was actively present as and when He choose. It was a reinforcement of the promise of verse 12. God would be revealed in the sovereign display of His power. God is a God of action, as is seen in the Exodus, as well as the Cross. This is His Name forever.

Elohim
This is the most common name for God found more than 2,500 times in the Old Testament. It comes from the early Hebrew word El. This is a general term for God which comes from the root ul meaning 'to be strong.' El first meant strength and then the strong one. It conveyed the idea of the power of God. Gradually El was lengthened to Elohim. This term speaks of God as the creator of all that is. Genesis 1:1 Elohim created the sun, moon and stars. It is also a plural name which does not means that there are many God's but rather that God possesses all of the possible divine attributes and powers. Elohim is greater than all gods Psalm 97:9 but also recognising that these gods are not real. Psalm 96:5

El Shaddai
This name for God generally means 'God Almighty'. In its full form it is found six times in the Pentateuch and once in Ezekiel. Genesis 17:1; 28:3; 35:11; 43:14; 48:3; Exodus 6:3; Ezekiel 10:5 It was the name used in the time of the Patriarchs. The shortened form of Shaddai is found more often in the Old Testament and used about 30 times in Job pointing to Job's early date. The word Shaddai comes from a root word sadad which means 'to deal violently with' or 'Destroyer'. There could be the element of judgment involved with this name. It conveys the idea of the All Powerful One. Usually the term is used in conjunction with a display of God's power in nature.

El Elyon
This name for God means God the Most High. It first appears in the account of Abraham's meeting with Melchizekek who is described as 'a Priest of God Most High.' Genesis 14:18 El Elyon is also mentioned in the rebellion of Satan. Satan said he wanted to be like El Elyon or God Most High. Isaiah 14:14 This name conveys the idea of God's rule and sovereignty.

El Olam
This name has come to mean the unchanging, eternal God. Genesis 21:33 The word Olam originally meant that which was hidden or concealed as in being unknown. The Jews would speak of the future in terms of Olam or eternity or everlasting. When the word is applied to God it conveys the idea of His immutability or his unchangableness. El Olam never changes. Psalm 100:5; Isaiah 40:28

Jehovah Jireh
 

This name means the God who provides or God will see to it. The Hebrew word transliterated jireh is actually a form of the common verb Ra'ah ('to see'). In Genesis 22:7 when Isaac asked Abraham where the lamb was for the burnt offering and Abraham replied, 'God himself will see to it,' he was declaring that God had everything under His control and would provide what was needed at the right time. This name point to Christ who is the ultimate Lamb which God provides. 

Adonai
This divine name translates as Lord. It means master and reflects the attribute of sovereignty. It means that God is the Lord who rules. Genesis 15:2,8 Whenever the Hebrew readers would come across the word Yahweh they would substitute Adonai in its place as Yahweh was too sacred to pronounce.

Misc. Names
 

Name	Meaning
El Roi	The Lord Our Shepherd
Elohim Qdhoshim	Holy God
Jehovah Sabaoth	The Lord of Hosts
Jehovah Nissi	The Lord our Banner
Jehovah M'quaddishkhem	The Lord who sanctifies
Jehovah Rophe	The God Lord who heals
Jehovah Tsidkenu	The Lord Our Righteousness
Jehovah Shalom	The Lord Our Peace
Jehovah Shammah	The Lord who is There

The Bible describes God also as Alpha and Omega, The beginning and the End. The Ancient of Days, Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace. He is described as the Judge, The Rock and High Tower. The Way the Truth and the Life. God of Abraham, Isaac and Jacob. King of Kings and Lord of Lords. The Bread of life, The resurrection and the life, the good shepherd. And many others. Each conveys a special aspect of Gods character.