Lant Carpenter (1811) on Matthew 28:19

Matt. xxvii. 19, ‘Go ye therefore, and teach all nations, baptizing them into εις the name of the Father and of the Son and of the holy spirit.’—On this passage I observe 1. “To be baptized into or in the name, is to be baptized into the faith or confession, or, in token of one’s faith and of one’s openly confessing. See Matt. xxvii. 19. Acts ii. 38. viii. 16. x. 48.” 2. He who was appointed by God as the agent in the Christian dispensation, was, under God, the most important person in the Christian dispensation. 3. In the preceding verse it is said, ‘all power is GIVEN To me in heaven and on earth,’ therefore this verse cannot be justly considered as implying the equality of the Son with the Father. 4. Baptizing into, or into the name of, a person is no proof of his divinity, otherwise Moses was God (See 1 Cor. x.2. ‘And all were baptized into Moses εἰς τὸν Μωϋσῆν in the cloud and in the sea.’ That to be baptized into any one, and to be baptized into his name, are phrases of the same signification, see Rom. vi. 3. Gal. iii. 27, compared with Acts xix. 5, &c. The passage from Galatians sufficiently indicates the meaning of the phrase, baptized into Christ, or, into the name of Christ: ‘For ye all are sons of God by faith in Christ Jesus: for as many as were baptized into Christ, did put on Christ.’) (Lant Carpenter, Unitarianism The Doctrine of the Gospel: A View of the Scriptural Grounds of Unitarianism [2d ed.; London: Richard Taylor and Co., 1811], 130-31)

Further Reading

Answering "God Loves Mormons" on The Trinity and

Old Testament Instances of "Name" Being Used for Multiple Persons