God reveals Himself to Moshe using a name He had not previously used when speaking to the Patriarchs or to the children of Israel. Moshe therefore wondered whether the nation would accept his message from God when using a name with which they were not familiar?
God's answer to Moshe is divided into three parts.
Firstly He says "I will be what I will be." (Exod. 3:14) As if to say, it doesn't matter what name He uses. In the second part of the answer, God says: "Ehyeh (I will be) has sent me to you." 'Ehyeh' seems to be the same name as the Divine name (shem hahavaya). The aleph was interchanged with the yod, and the yod was interchanged with the vav but the root of the two words is identical. When the word is spoken it is 'Ehyeh', and in the hidden form it is y-h-v-h. The third answer given by God is: "The Lord God of your forefathers, the God of Abraham, the God of Isaac, and the God of Jacob, has sent me to you." (Exod. 3:15) This is the most important answer, one which we say three times a day as the opening of the shmona esreh amida prayer.
Calling out to God, or knowing God, is difficult and beyond human understanding. Each person recognizes Him differently, depending on his spiritual level. The name can change, because the name is a function of the way in which a person recognizes God. God does not reveal Himself completely to any one person, because humans are transient beings. On the other hand, an entire nation can experience a revelation. The Jewish people's beliefs are based on their forefathers' experiences, and this connects them to God. It is therefore vital that the God who reveals Himself to them as a nation is the same God that their forefathers believed in.
Pharaoh searches for God calling His name, and since he doesn't know it, he says: "I do not know the Lord, neither will I let Israel out." (Exod. 5:2)
God opposes this view, He says to Moshe: "I will be what I will be." The specific name is not crucial, what is really important is that we know who He is, and not to place unnecessary emphasis on His name.