Alpha and omega are the first and the last letters in the Greek alphabet. The Greek alphabet was widely known at the time of Christ and its first use in the New Testament is found in the Book of Revelation, I am Alpha and Omega, the beginning and the ending, saith the Lord (Rev 1:8). The phrase signifies the beginning and the end, and thereby the eternal nature of Christ.
It may seem odd for the Savior to use a Greek phrase among the Nephites. Certainly, the Nephites did not know the Greek alphabet, but the phrase was a title and one of the many names of Christ. The use of titles which are language specific is not limited to this case. The name, Immanuel, is a Hebrew name which means God with us (Isa 7:14). While many recognize Immanuel as a name or title for Christ, few know its meaning because they are unfamiliar with Hebrew. Furthermore, the phrase Alpha and Omega has been used numerous times in the latter-day scriptures even though most latter-day saints are not much more familiar with the Greek alphabet than were the Nephites. (see DC 19:1; 35:1; 38:1; 45:7; etc.)