John certainly wasn’t saying the God was the God and the Logos was also the God, was he? That seems to be what you are saying if both times “God” appears in John 1:1 is definite, “THE” God.
In his typically enigmatic way, he is simply saying that not only was the Word as a person with God, but that the word was God as the Son having the same nature.
You can protest the puzzling phraseology, and try to make the Word out to be a god (or “was a god” if you want to press it), despite the problems that also entails, or you can see, if you could allow it, that the God whom Isaiah saw, and who of old hast laid the foundation of the earth, and whose work includes the heavens, and who essentially is the same, yesterday, today and forever, (Ps. 102:25-27; Heb. 1:10-12; 13:8) is the Son, who with the Father and the Spirit possess the same uncreated nature, the true God and eternal life. To God be the glory.