This is not a complicated question if one chooses to allow the Bible to speak on its own terms, allow related verses to inform the one in question, and resist the common method of making up new constructs or simply letting tradition rule over the Biblical text.
God is already adequately defined by Jesus and Paul as the Father. No further complexity need be added.
Now this is eternal life: that they know you, the only true God, and Jesus Christ, whom you have sent. (Jesus is praying to the Father)
1 Corinthians 8:6
yet for us there is but one God, the Father, from whom all things came and for whom we exist. And there is but one Lord, Jesus Christ, through whom all things came and through whom we exist.
Perhaps there is some weight to imagining all kinds of assumptions here, but that is not acceptable by a plain reading of the text and without causing contradictions with so many other verses. A Father, Son, and spirit God is simply a matter for those who like to imagine a God for themselves, relying on inference and conjecture, these are not hermeneutical principles. (Seeing the three mentioned in one verse (Matt 28:19 and a few others) is hardly verification of a triune God where all are eternal, equal, and of one substance)
The "word was with God". This means that we cannot presume to focus on the latter part of the verse, "the word was God" in isolation.
To have the word actually be God, means there are now two Gods if we retain the "with". This goes against all we are told, so there must be another solution.
The word cannot be God as God is God. God creates "through" the word. The word does nothing of itself. Whatever attributes it has, is because it carries the authority of God and does His bidding and decree.
This is affirmed by John in his epistle.
1 John 1:1-3
1 What was from the beginning, what we have heard, what we have seen with our eyes, what we have looked at and touched with our hands, concerning the Word (logos) of Life— 2 and the life was revealed, and we have seen and testify and proclaim to you the eternal life, which was with the Father and was revealed to us— 3 what we have seen and heard we proclaim to you also, so that you too may have fellowship with us; and indeed our fellowship is with the Father, and with His Son Jesus Christ.
Clearly, the word is not a 'who' and so this eliminates a 'person' with God. With the weight of OT understanding who understood there was only one God and a solitary God who is described with incessant consistency since Genesis. The word of God is His effect and power, distributing His creative actions according to every Godly decree without delay or equivocation. It is God’s own word and it does His bidding unpreventably!
The "word" became a person in Jesus.
Profoundly, the "word that became flesh" as Jesus, is not an automatic accomplishment of God’s will. Jesus had to choose to obey, to submit, to serve against his own will. It wasn’t automatic, it wasn’t easy, especially as the trial, torture, and crucifixion drew near. Jesus was not ready at his baptism to face the crucifixion; he had to learn to obey his God. Hebrews 5:8
There is one God who is the Father. The word is "with" God and so is not God as God is God but a representation of God, just as Jesus (the word enfleshed) is God's representative Hebrews 1:3, image and form.
Jesus, the ascended human without sin, the Lamb, and the 'Word of God' is still 'with' God because he is always shown (once ascended) to be at the side of God. We cannot help but be guided by the repeated truth that Jesus has the same God we do, John 20:17 and Revelation 3:12.