According to Daniel Ludlow, four different men named Joseph are referred to in 2 Nephi chapter 3 as follows:
(1) Joseph who was sold into Egypt; he is also known as Joseph the son of Jacob (Israel) -- verses 4-22.
(2) Joseph the son of Lehi -- verses 1-3, 22-25.
(3) Joseph Smith, Sr., the father of the prophet -- verse 15.
(4) Joseph Smith, Jr., the prophet -- verses 7-9,11,14-15,18-19.
[Daniel H. Ludlow, A Companion to Your Study of the Book of Mormon, p. 128]
2 Nephi 3:4 I am a descendant of Joseph who was carried captive into Egypt ([Illustration] “Joseph, our patriarchal ancestor, was prime minister of Egypt for 80 years. He lived approximately 1,771 to 1,661 B.C,” by A&OR. [W. Cleon Skousen, Treasures from the Book of Mormon, Vol. 1, p. 1200]
2 Nephi 3:4 I am a descendant of Joseph who was carried captive into Egypt. And great were the covenants of the Lord which he made unto Joseph (Illustration): Joseph of Egypt Making Grain Available during Famine. Artist: Robert T. Barrett. [L.D.S. Church, The Ensign, March 1990, inside front cover]
2 Nephi 3:4 I am a descendant of Joseph who was carried captive into Egypt ([Illustration] Joseph of Egypt. Joseph who was sold into Egypt saw the latter days. He spoke of Joseph Smith when he testified, “A seer shall the Lord my God raise up, who shall be a choice seer unto the fruit of my loins.” Artist: Robert T. Barrett. [Thomas R. Valletta ed., The Book of Mormon for Latter-day Saint Families, 1999, p. 78]
2 Nephi 3:4 I am a descendant of Joseph who was carried captive into Egypt. And great were the covenants of the Lord which he made unto Joseph ([Illustration] Joseph Making Himself Known to His Brothers. Artist: Ted Henninger. [L.D.S. Church, The Ensign, October 1987, inside back cover]