1 John 5:13 These things have I written unto you that believe on the name of the Son of God; that ye may know that ye have eternal life, and that ye may believe on the name of the Son of God.
In this verse John wants to remind us that all he has written so for is to remind us of the assurance we can have in our salvation. John wrote his gospel to bring people to Christ and he wrote this epistle to let people know they can be sure of their salvation. They are false teachers out there everywhere and they can shake you up and make you doubt you salvation but if we stay in the word and see where it tells us here we can be assured of our salvation then we will be OK. Eternal life is a relationship with the person of Jesus Christ and possessing His nature and know that the name of the Son of God, of course, is Jesus. There is power in that name. The name Jesus means Savior. To believe on the name Jesus means you believe there is salvation in the name.