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Yahweh: I AM. This name is generally considered to be the sacred Hebrew name of God and not meant to be spoken (according to the dictionary definition).
Elohim: This is generally understood to mean "The living God".
What we address God as is up to the speaker. It would probably be wise to address him with reverence and honor. Calling him "Abba" (father) would be appropriate, calling him "Lord", calling him "God", it's really just up to the person and their culture.