The 1838 Joseph Smith manuscript, the 1842 Times & Seasons (3: April 15, 1842, page 753), and the original edition of the Pearl of Great Price (1851, page 41) all state that the angel who appeared three times to Joseph Smith in 1823 was Nephi, not Moroni. The current canonized account of the history of Joseph Smith is from this same manuscript (albeit with a few editing changes, like substituting Moroni for Nephi).
Further documentation supporting the name of Nephi is found in the 1st edition of Lucy Mack Smith's Biographical Sketches of Joseph Smith the Prophet and His Progenitors for Many Generations, 1853, and John C. Whitmer's statement entitled "The Eight Witnesses", published in The Historical Record, Volume 7, October, 1888, page 621.
The latter document states, "I have heard my grandmother (Mary M. Whitmer - the mother of *five* BoM witnesses) say on several occasions that she was shown the plates of the Book of Mormon by an holy angel, whom she always called Brother Nephi."
It is argued by LDS apologists that the first four references cited above all propagate a transcription error committed during the 1838 manuscript recitation. That Joseph may have momentarily tangled the names, or perhaps the scribe did so. This error then apparently went undetected for 4 years, passed review for inclusion in the Times & Seasons, again was not corrected in any subsequent issue, and was picked up again in 1851 in the printing of the Pearl of Great Price. Also, Lucy Mack Smith then relied on Joseph's unedited history during that portion of her historical account.