D&C 20

From day one with the organization of the Church, we were instructed to maintain -

"...a list of the names of the several members uniting themselves with the church since the last conference; or send by the hand of some priest; so that a regular list of all the names of the whole church may be kept in a book by one of the elders, whomsoever the other elders shall appoint from time to time..."  (Doctrine and Covenants | Section 20:82)

I believe this to be one of the signs of the true Church.  Many other religious organizations cannot produce such a list. 

Even today as in days of old -

"...they were numbered among the people of the church of Christ; and their names were taken, that they might be remembered and nourished by the good word of God, to keep them in the right way, to keep them continually watchful unto prayer, relying alone upon the merits of Christ, who was the author and the finisher of their faith."  (Book of Mormon | Moroni 6:4)