What was the name of the Mormon Church?

~~ What was the name of the ~~
~~ Church of Jesus Christ of Latter-day Saints? ~~

Many times LDS missionaries and members of the LDS church will make the statement that the LDS church is a Christian church and the only true church of Christ on earth because even the name of the church bears the name of the Savior. But what if the church didn't always carry the name of the Savior? Would it no longer be his church? Read below and find out that for 4 years the LDS Church was named after it's members only.

2 And Jesus again showed himself unto them, for they were praying unto the Father in his name; and Jesus came and stood in the midst of them, and said unto them: What will ye that I shall give unto you?
3 And they said unto him: Lord, we will that thou wouldst tell us the name whereby we shall call this church; for there are disputations among the people concerning this matter.
4 And the Lord said unto them: Verily, verily, I say unto you, why is it that the people should murmur and dispute because of this thing?
5 Have they not read the scriptures, which say ye must take upon you the name of Christ, which is my name? For by this name shall ye be called at the last day;
6 And whoso taketh upon him my name, and endureth to the end, the same shall be saved at the last day.
7 Therefore, whatsoever ye shall do, ye shall do it in my name; therefore ye shall call the church in my name; and ye shall call upon the Father in my name that he will bless the church for my sake.
8 And how be it my church 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.
Red added to emphasize the alleged words of Christ.

From the beginning of the Mormon Church on April 6, 1830 to May 3, 1834, the name of the church was the "Church of Christ".

BOOK

COMMANDMENTS,

FOR THE GOVERNMENT OF THE

Church of Christ,

ORGANIZED ACCORDING TO LAW, ON THE

6th of April, 1830

========================

ZION:

PUBLISHED BY W. W. PHELPS & CO.

...........
1833

From April 26, 1838 to the present it has been known as "The Church of Jesus Christ of Latter-day Saints" as named in the revelation in Doctrine and Covenants 115:3.

But what was the named from May 3, 1834 to April 25, 1838, a period of almost four years? At a conference of Elders on May 3, 1834, with Joseph Smith, Jr. as moderator, the name "The Church of the Latter Day Saints" was adopted by unanimous vote.
(The Evening and Morning Star, Vol 2 No. 20, page 160, May 1834, and History of the Church 2:62.)

This is the Title Page to the 1835 edition of the Doctrine and Covenants. The name of the church is shown here to be

THE CHURCH OF THE

LATTER DAY SAINTS:

...therefore ye shall call the church in my name;....And how be it my church save it be called in my name?..." (3 Nephi 27:7-8)

They said this was the reason their Church's name was "The Church of Jesus Christ of Latter-day Saints".

Mormon Apostle Bruce R. McConkie said, "One or more of the names of Christ has always been used in the formal name of the Church." (Mormon Doctrine, 1979 edition, page 136)

Mormon Apostle James E. Talmage said the following about 3 Nephi 27:4-8,
In such wise did the Lord confirm as an authoritative bestowal, the name which, through inspiration, had been assumed by His obedient children, The Church of Jesus Christ. The Lord's explanation as to the one and only Name by which the Church could be appropriately known is cogent and convincing. It was not the church of Lehi or Nephi, of Mosiah or Alma, of Samuel or Helaman; else it should have been called by the name of the man whose church it was, even as today there are churches named after men; but being the Church established by Jesus Christ, it could properly bear none other name than His." (Jesus the Christ, 1973 edition page 737)

Does this mean that for almost four years, since they did not have the name of Christ, they were NOT Christ's church? Does this mean they rejected Christ? According to 3 Nephi 27:6-8 and Apostles McConkie and Talmage they did. Why couldn't they get their name right in the first place, if it was divinely inspired?