To directly answer your question I "DO NOT" know of any denominations that insert the name Jesus in the text of John 1:1. However, we do learn after John 1 that it is the person of Jesus Christ who became flesh at John 1:14. Moreover, John the Baptist bore witness of Him. Who do you think the "Him" is? John the Apostle answers that question at John 1:17.
Also, it's not hard to arrive by deductive reasoning that John 1:1 is referring to Jesus Christ/the Messiah. If the verse is "isolated" no one would know who it refers without any context. Some might guess and say it could be the Messiah.
Getting back to John 1:1, please note at John 1:1 that it says "the" (definite article) Word (singular) existed. It doesn't say God's word or words, it says "The Word existed..." And "The Word existed how? The Word existed with the God.
In John 1Lb The Word and The God are distinct, there is a subject/object distinction between the two. Finally, "The Word was God." So whatever God is, The Word is, and vice versa. So if "The Word" is impersonal, God is impersonal...if "The Word" is just a thought or a plan, then "The God" is just a though or a plan. But remember, "The Word" singular existed and "the Word" is not "The God" in John 1:1b.
That said, "word" which in the Greek here is "Logos," is in Aramaic "Memra." In the Jewish Targums, "The Memra of God' was used in place of "God" in many places, such as places where "God" is used two times in the same passage but seems to be oppositional, such as "the Lord rained fire and brimstone on Sodom and Gomorrah from the Lord out of Heaven," the former would be "the Memra." Sometimes for the Angel of the Lord.
In the Targum the Memra figures constantly as the manifestation of the divine power, or as God's messenger in place of God Himself, whenever the predicate is not in conformity with the dignity or the spirituality of the Deity. (For a fuller treatment of this you can read The Gospel of the Memra by Jewish scholar Daniel Boyarin.)
Since you were the one that raised the question about the beginning at John 1:1 what beginning is this referring? You claim to be a Unitarian and I was told that the beginning at John 1:1 refers to the "New Beginning" when Jesus arrived and incarnated. This means that even you believe that John 1:1 refers to Jesus.
Genesis 1:1 states, "In the beginning God created the heaven's and the earth" (NKJV). John 1: says, "In the beginning was the Word, and the Word was with God, and the Word was God."
Both verses start out with the same three words, "In the beginning." Yet the main thought in Genesis 1:1 is on WHAT HAPPENED "in the beginning," and in John 1:1 the emphasis is on WHO EXISTED "in the beginning."
John 1:3 is an emphatic statement declaring that Jesus Christ, before His incarnation, had made everything in the universe. He is the God of Genesis 1:1, the God of all creation. Furthermore, note that "all things were made by Him, and apart or without Him nothing came into being that has come into being." (Some of these comments were made by the "Institute of Creation Research).