'Name' in the Bible

I am writing to you, little children (believers, dear ones), because your sins have been forgiven for His name’s sake [you have been pardoned and released from spiritual debt through His name because you have confessed His name, believing in Him as Savior].

This is His commandment, that we believe [with personal faith and confident trust] in the name of His Son Jesus Christ, and [that we unselfishly] love and seek the best for one another, just as He commanded us.

These things I have written to you who believe in the name of the Son of God [which represents all that Jesus Christ is and does], so that you will know [with settled and absolute knowledge] that you [already] have eternal life.