A.T. Robertson Commentary 1 John 3:23

"And this is his commandment, that we should believe in the name of his Son Jesus Christ, and love one another, even as he gave us commandment." — 1 John 3:23 (ASV)

His commandment (η εντολη αυτου).

That (ινα). Subfinal use of ινα in apposition with εντολη (commandment) and explanatory of it, as in Joh 15:12 (εντολη ινα). See Christ's summary of the commandments (Matthew 22:34–40). So these two points here (1)

We should believe (πιστευσωμεν, first aorist active subjunctive according to B K L, though Aleph A C read the present subjunctive πιστευωμεν) either in a crisis (aorist) or the continuous tenor (present) of our lives. The "name" of Jesus Christ here stands for all that he is, "a compressed creed " (Westcott) as in 1:3. Note dative ονοματ here with πιστευω as in 5:10, though εις ονομα (on the name) in 5:13; John 1:12; 2:23; 3:18. But (2) we should love one another" (αγαπωμεν αλληλους), as he has already urged (2:7f.; 3:11) and as he will repeat (4:7,11f.; 2 John 1:5) as Jesus (even as he gave us commandment, that is Christ) had previously done (John 13:34; 15:12,17). There are frequent points of contact between this Epistle and the words of Jesus in Joh 13-17.