“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.”
‭‭1 John‬ ‭5‬:‭13‬ ‭KJV‬‬

Jesus expected every believer to live by his name, because in their name, they would face certain limitations, not just physically (because the man who bares the name of the king, Governor or President of a territory, state or country where he resides would face very limited physical oppositions) but spiritually, but because his name is above every name and transcends time, distance and dimensions (earth, heaven, under the earth, Philippians 2:9-10), there is no limitation to be faced, instead they become invisible to the corruption and vices on the earth and live their lives as helpers of men sent from God:
“And these signs shall follow them that believe; IN MY NAME shall they cast out devils; they shall speak with new tongues; they shall take up serpents; and if they drink any deadly thing, it shall not hurt them; they shall lay hands on the sick, and they shall recover.” Mark‬ ‭16‬:‭17‬-‭18‬
So the Bible tells us: Colossians‬ ‭3‬:‭17‬.
Being conscious of the name you now bear is important to God, no wonder he says continually speak about the greatness of and give thanks to his name.

Bible Reading Plan: Psalm 43 and 44