The record was named for Mormon because it was he who took all of the writings of those who previously kept the record and condensed them into what we have today. He took the most precious parts and included those things that we would need for our salvation. (See Words of Mormon 3-6)
Because we believe The Book of Mormon to be the word of God, the name "Mormon" has been associated with the Church. However, it is not and never has been the Church of Mormon nor the Church of Joseph Smith. It has always been The Church of Jesus Christ. It is Jesus Christ who sits at the head of the Church and it is Jesus Christ who we worship as our Savior. Ephesians 5:23 states, " . . .even as Christ is the head of the church: and he is the saviour of the body." Other men, such as Abraham, Moses, Noah, have helped to preach the gospel and administer in the ordinances of it, but have never been who we worship. Many have falsely believed that we worship Joseph Smith. " . . . there is none other name given under heaven save it be this Jesus Christ, of which I have spoken, whereby man can be saved." (2 Nephi 25:20)
While we are commonly called "Mormons" it should always be understood that we acknowledge and worship only Jesus Christ as our Savior and Redeemer, and that it is only through His name that we may be saved. " And we talk of Christ, we rejoice in Christ, we preach of Christ, we prophecy of Christ, and we write according to our prophecies, that our children may know to what source they may look for a remission of their sins." (2 Nephi 25:26)