1 John 3:23

The apostle, having mentioned keeping the commandments, and pleasing God, as the qualification of effectual petitioners in and with Heaven, here suitably proceeds, I. To represent to us what those commandments primarily and summarily are; they are comprehended in this double one: And this is his commandment, That we should believe on the name of his Son Jesus Christ, and love one another, as he gave us commandment, Jo1 3:23. To believe on the name of his Son Jesus Christ is, 1. To discern what he is, according to his name, to have an intellectual view of his person and office, as the Son of God, and the anointed Saviour of the world. That every one that seeth the Son, and believeth on him, may have everlasting life, Joh 6:40. 2. To approve him in judgment and conscience, in conviction and consciousness of our case, as one wisely and wonderfully prepared and adapted for the whole work of eternal salvation. 3. To consent to him, and acquiesce in him, as our Redeemer and recoverer unto God. 4. To trust to him, and rely upon him, for the full and final discharge of his saving office. Those that know thy name will put their trust in thee, Psa 9:10. I know whom I have believed, and I am persuaded that he is able to keep that which I have committed unto him against that day, Ti2 1:12.

— Matthew Henry's Concise Commentary (public domain)

Summing up of God's commandments under the Gospel dispensation in one commandment. this is his commandment--singular: for faith and love are not separate commandments, but are indissolubly united. We cannot truly love one another without faith in Christ, nor can we truly believe in Him without love. believe--once for all; Greek aorist. on the name of his Son--on all that is revealed in the Gospel concerning Him, and on Himself in respect to His person, offices, and atoning work. as he--as Jesus gave us commandment.

— Jamieson-Fausset-Brown Commentary (public domain)