Cheryl Schatz

Here is proof that the early church fathers saw the term the incarnated Lord as “Christ” where God is His head.

32. But the saying, that in respect of the Incarnation God is the Head of Christ, leads on to the principle that Christ, as Incarnate, is the Head of man, as the Apostle has clearly expressed in another passage, where he says: “Since man is the head of woman, even as Christ is the Head of the Church;”26 whilst in the words following he has added: “Who gave Himself for her.”27 After His Incarnation, then, is Christ the head of man, for His self-surrender issued from His Incarnation.
33. The Head of Christ, then, is God, in so far as His form of a servant, that is, of man, not of God, is considered, But it is nothing against the Son of God, if, in accordance with the reality of His flesh, He is like unto men, whilst in regard of His Godhead He is one with the Father, for by this account of Him we do not take aught from His sovereignty, but attribute compassion to Him.
    Schaff, P. (1997). The Nicene and Post-Nicene Fathers Second Series Vol. X (266).