If we had the time, I could show you many verses where God shows the rewards that are going to go to those who glorify His name. Remember that we do that (i.e., break the third commandment) not just with what comes out of our mouth - swear words. That is just one small part of it. God is interested in the whole landscape of our witness for Him - the conduct of our lives in every area, and even our attitudes. Do they live up to (are they holding up the reputation of) the name, which we now bear?
What John is doing here is calling upon these people to remember their privileges in bearing the name of God.
That is what John is doing here in I John. It is a gentle reminder to those of us who bear the name of God - to purify ourselves and uphold that name. There might be what could be considered a paradox here. We think that, in order to know God, we have to see Him. In order to be like Him, we have to see Him. But God says, No. He has not given us opportunity to see Him. And we are not going to see Him until He chooses to reveal Himself to us this way. Instead, God has chosen to operate His purposes by faith. He has revealed what He is (1) through a multitude of circumstances, (2) through His names, and (3) especially by the life of Jesus Christ. And, by faith, He wants us to emulate Him by means of His Spirit. The power is there to do it.
Brethren, I feel confident that if we saw Him in the flesh (that is, our flesh - not His flesh), if we saw Him while we were still flesh and blood, either one of two things would happen. We would be so over-awed by His holiness, by His purity, that we would just give up and quit right there. Or, our curiosity would be satisfied and we would give up even there. God's way is best. He knows what He is doing. He wants us to emulate Him and uphold His name through the revelation that is coming through Jesus Christ.