I am not such a deep scholar that I can totally answer that question. Also, I'm not so sure that the deepest scholar can fully explain the nature of God. But this we know:
Therefore God has highly exalted him and bestowed on him the name that is above every name, so that at the name of Jesus every knee should bow, in heaven and on earth and under the earth, and every tongue confess that Jesus Christ is Lord, to the glory of God the Father. (Philippians 2:9-11)
But to keep the discussion rolling, there are some connections to Yahweh in the Old Testament and Jesus. For example, in Exodus 33:14-15 Yahweh says that He will give rest. Jesus makes the same claim in Matthew 11:28-30.
Deuteronomy 30:20 says that Yahweh is our life. Colossians 3:3-4 makes the same claim for Jesus. There are many more examples.
Regarding the Holy Spirit, in scripture it talks about the Holy Spirit of Yahweh. But to debate whether or not the Holy Spirit is Yahweh can be a bit confusing.