The full name of the church is actually The Church of Jesus Christ of Latter-day Saints.
In part, it comes from 1 Corinthians 1:2 which says "Unto the church of God which is at Corinth,
to them that are sanctified in Christ Jesus, called to be saints, with all that in every place call upon the name of Jesus Christ our Lord,
both theirs and ours."
A more full explanation comes from the Book of Mormon in 3 Nephi 27:8 which says "And how be it my bchurch save it be called in my name? For if a church be called in Moses' name then it be Moses' church; or if it be called in the name of a man then it be the church of a man; but if it be called in my name then it is my church, if it so be that they are built upon my gospel."
H-D