We are Adopted into God's family because of his Name while some remain children of the Devil (John 8:44).
John 1:12 But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
John 8:44 Ye are of your father the devil, and the lusts of your father ye will do. He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar, and the father of it.
Sons of God - Children of God by adoption. Christians are called sons of God:
1. Because they are “adopted” by Him, 1 John 3:1.
2. Because they are “like Him;” they resemble Him and have His spirit.
3. They are united to the Lord Jesus, the Son of God, are regarded by Him as his brethren Matthew 25:40, and are therefore regarded as the children of the Most High.
On his name - This is another way of saying believeth in “him.” The “name” of a person is often put for the person himself, John 2:23; John 3:18; 1 John 5:13. From this verse we learn:
1. That to be a child of God is a privilege - far more so than to be the child of any human being, though in the highest degree rich, or learned, or honored. Christians are therefore more honored than any other persons.
2. God gave them this privilege. It is not by their own works or deserts; it is because God chose to impart this blessing to them, Ephesians 2:8; John 15:16.
3. This favor is given only to those who believe on him. All others are the children of the wicked one, and no one who has not “confidence in God” can be regarded as his child. No parent would acknowledge one for his child, or approve of him, who had no confidence in him, who doubted or denied all he said, and who despised his character. Yet the sinner constantly does this toward God, and he cannot, therefore, be called his Son. (Albert Barnes Notes on the Bible)
There is Salvation in His Name:
Acts 4:12 Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.
Neither is there salvation - The word “salvation” properly denotes any “preservation,” or keeping anything in a “safe” state; a preserving from harm. It I signifies, also, deliverance from any evil of body or mind; from pain, sickness, danger, etc., Acts 7:25. But it is in the New Testament applied particularly to the work which the Messiah came to do, “to seek and to save that which was lost,” Luke 19:10. This work refers primarily to a deliverance of the soul from sin Matthew 1:21; Acts 5:31; Luke 4:18; Romans 8:21; Galatians 5:1. It then denotes, as a consequence of freedom from sin, freedom from all the ills to which sin exposes man, and the attainment of that perfect peace and joy which will be bestowed on the children of God in the heavens. (Albert Barnes Notes on the Bible
There is the Remission of Sin In His Name:
Acts 10:43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.
Thayers' Greek Definition: Remission
1) release from bondage or imprisonment
2) forgiveness or pardon, of sins (letting them go as if they had never been committed), remission of the penalty
We are Baptized In Jesus Name:
Acts 2:38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
Repent, and be baptized. For the first time the terms of pardon under the New Covenant and the Great Commission are given; given once for all time, and always the same. The convicted, broken-hearted, sorrowing sinner, believing that Jesus is the Christ, is to repent and be baptized.
Repent. Not sorrow. They already sorrowed; but a change of purpose; the internal change which resolves to serve the Lord. The Greek term rendered repent, means a change of mind. The act of obedience in baptism is an outward expression of both faith and repentance.
In the name of Jesus Christ. "Upon the name" (Revised Version). Upon the ground of the name. In submission to the authority of Jesus Christ.
For the remission of sins. Thus, by complying with the conditions just named, they shall receive remission of sins. No man can receive pardon without faith and repentance, nor can he without submission to the will of Christ. "Eis (for) denotes the object of baptism, which is the remission of the guilt contracted in the state before metanoia (repentance)."--Meyer. "In order to the forgiveness of sins we connect naturally with both the preceding verbs. This clause states the motive or object which should induce them to repent and be baptized."--Prof. Hackett.
The gift of the Holy Spirit. Promised as a comforter to all who obey Christ, but whom "the world cannot receive. (The People's New Testament, BW Johnson)