If we translate the name Yahweh, which I think means I am, this has no meaning. God said to Moses when he asked Him to reveal His name so that he can say to the children of Israel who God was. God said tell them I am sent you. Do you think the answer that God gave to Moses, "I am" is why we associate Him with so many names.

I think I understand why you are confused. According to Gail Riplinger, in her book In Awe of Thy Word, the Lord’s name Jehovah was changed to Yahweh by some German Bible critics during the 19th century. The reason why they tried to convince people that the God of Hebrews was named Yahweh is because they wanted people to believe that the God of the Hebrews was the same god as the pagan deity Yaho. This, according to their plan, has caused a great deal of confusion (and we know that “God is not the author of confusion”). I think you may have been one of their victims.

God’s name I AM does indeed have meaning. It emphasizes the fact that the Lord God is eternal. Only He can rightly use that name. All other deities have had some beginning. Even the devil himself was created at some point in time (Ezekiel 28:13-15 [13] Thou hast been in Eden the garden of God; every precious stone was thy covering, the sardius, topaz, and the diamond, the beryl, the onyx, and the jasper, the sapphire, the emerald, and the carbuncle, and gold: the workmanship of thy tabrets and of thy pipes was prepared in thee in the day that thou wast created. [14] Thou art the anointed cherub that covereth; and I have set thee so: thou wast upon the holy mountain of God; thou hast walked up and down in the midst of the stones of fire. [15] Thou wast perfect in thy ways from the day that thou wast created, till iniquity was found in thee.
See All...). John 1:1In the beginning was the Word, and the Word was with God, and the Word was God.
See All... says, “In the beginning was the Word, and the Word was with God, and the Word was God.” It is obvious that the Word is Jesus Christ as we read further in this passage. When time began, He was already present. He had no beginning and has no end. He is eternal and therefore everything associated with Him is eternal—His word, His salvation, His life, His glory, His power, His judgment, His inheritance, etc.

The name I AM is so important and meaningful that when Jesus Christ used it, His enemies tried to stone Him—“John 8:58-59 [58] Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am. [59] Then took they up stones to cast at him: but Jesus hid himself, and went out of the temple, going through the midst of them, and so passed by.
See All... “Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am. Then took they up stones to cast at him: but Jesus hid himself, and went out of the temple, going through the midst of them, and so passed by.” This is one of the ways that proves that Jesus Christ is Jehovah of the Old Testament. The JW's (Jehovah Witnesses) do not believe that Jesus Christ was the eternal Son of God, the God who spoke to Moses on Mount Sinai. But Christ’s enemies knew exactly what He was saying. He was identifying Himself as the God of the Old Testament, “the King eternal, immortal, invisible, the only wise God” (1 Timothy 1:17Now unto the King eternal, immortal, invisible, the only wise God, be honour and glory for ever and ever. Amen.
See All...).

I think that you are exactly right with your last question. The name I AM causes us to associate Him with many of His other names. He said, “I am the way, the truth, and the life” in John 14:6Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me.
See All..., “I am the good shepherd” in John 10:11I am the good shepherd: the good shepherd giveth his life for the sheep.
See All..., “I am the resurrection and the life” in John 11:25Jesus said unto her, I am the resurrection, and the life: he that believeth in me, though he were dead, yet shall he live:
See All..., “I am the light of the world” (John 9:5As long as I am in the world, I am the light of the world.
See All...), “I am the door” (John 10:9I am the door: by me if any man enter in, he shall be saved, and shall go in and out, and find pasture.
See All...), “I am the Son of God” (John 10:36Say ye of him, whom the Father hath sanctified, and sent into the world, Thou blasphemest; because I said, I am the Son of God?
See All...), “I am the true vine” (John 15:1I am the true vine, and my Father is the husbandman.
See All...), etc.

I hope this helps your understanding of that “name which is above every name” (Philippians 2:9Woe to him that coveteth an evil covetousness to his house, that he may set his nest on high, that he may be delivered from the power of evil!
See All...) our Lord and only Saviour Jesus Christ.