correct.As i wrote previously:
God is a single “actor,” with a single will. Everything God does is an act of the entire Trinity, acting as one, not as a committee.
Here is an example of how the One God, the Trinity in essense, works as One:
Acts 5:30 “The God of our Fathers raised up Jesus”…
= the Father
Rom.8:11" But if the Spirit of him that raised up Jesus from the dead…
=The Holy Sirit
John.2:19 …Destroy this temple and I will raise it up."
= The Son
wether we say the Father, His Word or His Spirit, we are talking about the One God,
One actor that did and does everything through His Word and Spirit starting Genesis. We explain the Oness in terms of Word/ Spirit because scripture explains it since the OT. So when we talk about the Trinity, it is in terms of theology in order to explain the Oness of God through scriptures.
we do not “name”. We explain the NATURE of the One God as revealed in OT and NT. The Psalmist, for example, talked clearly about the Spirit of God = God. Did we invent or name it?no. It is God who revealed about His Spirit= Him, not us. We simply explain about the Holy Spirit and we say it is a “person” in the sense that it is God, not an impersonal power. God reveals, we explain what is revealed in light of the OT and how Jesus revealed and explained what was not understood or was not yet fulfilled. After Jesus explained did the apostles understand who the Messiah really is, and not from their misunderstanding of the OT. The apostles themselves thought he will be an earthly king who will save them from their ennemies but Jesus opened their eyes to the correct understanding of scripture.
ever heard the saying " wherever there are 2 Jews, there are 3 opinions"?

the Jews do not have all the answers you think they can have from reading the OT. Jesus fulfilled and explained, but some rejected, hence they got the introduction and plot (OT), but got no ending (NT). The ending is that God came as the savior, the King, the Messiah, to save when they expected the Messiah to be an earthly king. The Messiah was indeed a King, but Jesus explained in what sense He was a King. He was the King of this world, not an earthly King, and He refused to be ordained as king (read NT) because, exactly, He is the King of this world, not an earthy one as Jews expected, and the King of the Kings came to save, not from the ennemies, but to save the souls from satan, the real ennemy, by nailing all sins to the cross(final atonement) and giving a new life, a new mannah to eat , a New Covenant (= good news of salvation fulfilled). They got the description correct in some sense, but not who the Messiah, the Savior , is.
Jesus told them He will not explain heavenly things cuz they don’t even understand the earthly ones. And yes, the Holy Spirit is God according to Jews, it is surely not an angel. But Jews do not believe in the Word incarnate, so you can say they believe in the Father and His Holy Spirit (without explaining much about the Holy Spirit as we do) , and they do believe the Word of God is God but they do not believe the Word of God was incarnate as the Messiah.