Many expecting parents pore through baby books looking for that perfect name that would fit their baby. Some name them before they are born. Others wait a few days after they are born. In scripture, names are more than just nomenclature to distinguish one person from another. Names were indications of what a person is like. This is why Jesus changed Simon's name to Peter, the "Rock."
God gives his name, "Yahweh" to Moses in Exodus 3:14-15. He calls it his name of remembrance for all generations. Many scholars have tried to identify the precise meaning of the name over the years. It is an antiquated Semitic form of the word, "to be." Using another form of the same word, God says, "I am who I am," which could also be translated, "I will be who I will be." In fact, the exact same word in the exact same form occurs in verse 12, when God tells Moses, "I will be with you." God is making a promise to empower, strengthen, and equip Moses for whatever challenge is before him. Whether it is blood turning to water or water dividing so they can cross over, God will be with them all the way.
God refers to his name as His "memorial name" or "name of remembrance." Therefore, there is much more to his name than just a definition. When God reveals his name, he reminds them of his character, the type of God he is, and what he had done for them. This is why he begins the covenant with "I am Yahweh your God, who brought you out of the land of Egypt, out of the house of slavery" (Ex 20:2). Yahweh is the God who comes down to redeem his people. Yahweh is the God who binds himself in a covenant of promise to his people. Yahweh is the God who is faithful, trustworthy, and gracious. Yahweh is the God who speaks to, acts on behalf of, and sacrifices for his people. Yahweh is the God who comes near. This is some of the "meaning" behind his name.
Perhaps more significant than the precise definition of Yahweh's name is simply the fact that He provides his name. People do not offer their name arbitrarily, but usually only in order to initiate some sort of relationship. After God offered his name, His people can call upon him not just by designations, such as God or Lord, but by his name, Yahweh. This is remarkable for several reasons. When one gives out his name to someone and initiates a relationship, there is a risk involved. One risks having his name dishonored by the person he is revealing his name to. He also risks being subject to wants, needs, and desires of the one his is giving his name to. He also risks being hurt by that person. In short, he becomes vulnerable. This is exactly what God knowingly did. How many times has God experienced grief, sorrow, anger, and agony as a result of his relationship with us? Imagine the physical, emotional, and spiritual pain he felt at the cross. Yet, in spite of all this, God gives his name.
All of this reveals that God is inherently a relational God. He is not aloof or emotionally removed from his creation. He is a God who identifies with, sympathizes with, and shares with us. In short, God is love. Since God is love, we also ought to love as he loved.