There is a song (hymn) called Only in the Name of Jesus that in its lyrics has that phrase. It is based on a bible verse in the book of Acts (4:12) that says, “Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.”
That is a powerful verse. It literally says that the only way to get saved is through the name of Jesus. You can’t call on any other name for the sake of salvation.
I know a lot of people that do not like to hear the name of Jesus and I think it is because to accept that Jesus is the son of God AND to accept that he is the only way to get to heaven is not something they want to do. They would rather just call on God, or as they say in AA: ‘The God of my understanding’, or ‘A Higher Power.
I am a born again Christian and believe in Jesus. I believe I am saved through a few steps I took but mostly I from the verse: “For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life.” John 3:16