I think this is a logical mistake more than a theological mistake, and I don't think this is a named heresy. If anything, it seems like a violation of the communication of properties; something reminiscent of patripassianism.
The Shield of the Trinity (see below) is basically a picture version of the communication of properties, which sets up the background:
- Th Father is God
- The Son is God
- The Holy Spirit is God
- The Father is not the Son and is not the Holy Spirit
The equality is based on ontology and essence (homoousia), and their inequality is based on their function and their personhood (hypostasis). The former is required of a monotheistic God, and the latter is required of a Triune God.
The relavent logical principles are the law of non-contradiction and law of identity.
- A = A (identity)
- A ≠ ~A (non-contradiction, where ~A is read as "not A")
- The Father is Father to the Son, and the Son is Son to the Father. The same type of relationship does not exist with the Holy Spirit. Jesus couldn't be said to be the Son of the Holy Spirit.
- Since Jesus is not the Father (patripassianism), Jesus is not a Father to any person of the Trinity and therefore not to Himself.
- Jesus is the Son of God, but not the Son of Jesus. Communication of properties does not mean that you can replace any person with the Trinity with God or vice versa. That is why the shield of the Trinity exists. Another example would be saying that Mary is the "Holy Spirit-bearer" rather than "Christ-bearer" or "God-bearer."
- Jesus being the Son of Himself is incoherent and logically invalid. The only way that this could work is if the law of non-contradiction was violated such that Jesus could be equal to the Father (to be Son of Himself) and not equal to the Father (to not violate the communication of properties), which does not compute.
The topics of the eternal generation of the Son and the procession of the Holy Spirit are related and also discussed in the resources below. They help draw out the ideas of Jesus being the Son and the relations between the persons of the Trinity, etc.
Systematic Theology by Augustus Hopkins Strong
Dogmatic Theology by W.G.T. Shedd
Shield of the Trinity: