English: King James Version
In the Bible, someone’s name represents all of their qualities, their character and attributes as a whole. So people who "believe on the Lord’s name" are not just accepting that He is who He is; they are seeing Him as God, believing in what He taught and adopting it into their lives. And since Jesus represents the divine truth, or the deepest expression of the Lord’s love, it means that we today can become "sons of God" if we open ourselves to the Lord’s love and all it teaches us, and practice that love toward others.
And what is a "son of God"? It does not mean that we will be what Jesus was, but it does mean that we will be what the Lord hopes for us to be. The case is this: When we are born of our parents, we inherit a spectrum of spiritual weaknesses and challenges, places where we are subject to temptation. But if we open ourselves to the Lord and follow His teachings, we can eventually be "born" again, with the evil desires stripped away so that we can live in peacful, loving joy to etenity. This is what is meant here by "sons of God" – if we receive the Lord and follow him we can become angels, dwelling in eternal happiness.
(References: Apocalypse Explained 151 ; Apocalypse Explained 745 ; Arcana Coelestia 9241, 9454; Arcana Coelestia 1608 ; Arcana Coelestia 2531 ; Arcana Coelestia 8409 ; Doctrine of the Lord 18 )
Explanation(s) or references from Swedenborg's works:
Conjugial Love 129
Divine Providence 230
Canons of the New Church 16
De Verbo 20