In Doctrine and Convenants Section 115:3,4 Christ directed that His Church be named "The Church of Jesus Christ of Latter-day Saints found here
lds.org/scriptures/dc-testament/dc/115?lang=eng
3 And also unto my faithful servants who are of the high council of my church in Zion, for thus it shall be called, and unto all the elders and people of my Church of Jesus Christ of Latter-day Saints, scattered abroad in all the world;
4
For thus shall my church be called in the last days, even The Church of Jesus Christ of Latter-day Saints.
The LDS Bible dictionary here
lds.org/scriptures/bd/saint?lang=eng&letter=s defined a “Saint” as…
The word saint is a translation of a Greek word also rendered “holy,” the fundamental idea being that of consecration or separation for a sacred purpose; but since what was set apart for God must be without blemish, the word came to mean “free from blemish,” whether physical or moral. In the New Testament the saints are all those who by baptism have entered into the Christian covenant (see Acts 9:13, 32, 41; Rom. 1:7; 1 Cor. 1:2; Philip. 1:1; 1 Pet. 1:14–15). See also Holiness.
So, a Latter-day Saint would be someone who entered into the covenant of baptism in the last days. (And for the record, LDS only view baptism in the LDS church as valid since we believe that only the LDS church possess the authority to administer the ordinance of baptism.)
I hope this helps…
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