I can answer this for one particular group of non-trinitarians: the "Swedenborgian" denominations that accept the Christian theology of Emanuel Swedenborg (1688-1772). Swedenborg rejected the traditional doctrine of the Trinity, saying that God is not three persons, but one person, in which the Father, Son, and Holy Spirit are three "essential components" (Latin essentialia). (For a Swedenborgian presentation of the Biblical basis against the doctrine of the Trinity, along with a brief explanation of Swedenborg's non-trinitarian doctrine of the Father, Son, and Holy Spirit as together constituting one person of God, see: What is the Biblical basis for disbelief in the doctrine of the Trinity?)
For those who accept Swedenborg's theology, "the Son of God" is not a separate person, but rather the human manifestation of God's eternal divine nature (which is called "the Father" in the New Testament). "The Son of God" is also the divine truth, which is called "the Word" in John 1:1, 14:
In the beginning was the Word, and the Word was with God, and the Word was God. . . . The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth.
Here is how Swedenborg states the meaning of "the Son of God" as God's human manifestation, in True Christianity #92:
The "Son of God" is the human manifestation in which God sent himself into the world. The Lord [Jesus] frequently says that the Father "sent" him, or that he "was sent" by the Father (for example, Matthew 10:40; 15:24; John 3:17, 34; 5:23, 24, 36, 37, 38; 6:29, 39, 40, 44, 57; 7:16, 18, 28, 29; 8:16, 18, 29, 42; 9:4; and very often elsewhere). The Lord says this because "being sent into the world" means coming down among people, which he did through the human manifestation he took on through the Virgin Mary.
The human manifestation really is the Son of God, in that he was conceived by Jehovah God as the Father, as it says in Luke 1:32, 35. (links added)
Here is how Swedenborg states the meaning of "the Son of God" as divine truth, in Arcana Coelestia (Secrets of Heaven) #7499 (in a somewhat archaic translation):
In the Word [the Bible] the Lord is called "Jehovah" in respect of Divine Goodness, for Divine Goodness is the Divine itself, and the Lord is referred to as "the Son of God" in respect of Divine Truth. For Divine Truth goes forth from Divine Goodness, as the Son does from the Father, and is also said to be born from it. But something more must be said to show what this implies. When the Lord was in the world He made the Human He had assumed Divine Truth, and at that time called Divine Goodness, which is Jehovah, His Father. He did so because, as has been stated, Divine Truth goes forth and is born from Divine Goodness.
In other words, "the Father" is the divine good, or the divine love; and "the Son" is the divine truth, or the divine wisdom. Together with the Holy Spirit—which, in Swedenborg's theology, is "the divine proceeding," or in contemporary language, God's love and truth flowing out into the universe with power—these three "essential components" constitute the single person of God.