Rabbi Yitzchok Alfasi was known as the Rif. The Roshei Teivos of his name is רי"א, and as far as I know there is no other historic figure known as the רי"א. Then why was he known as the Rif?
Because "Alfasi" is really "al-Fasi". "Al-Fasi" is Arabic for "the Fezite" (Fez being the city in Morocco where he lived).
So kind of like how the word "of" gets swallowed in "USA", the word "the" got swallowed in "Rif". Wouldn't have made much sense to make his acronym stand for "Rabbi Yitzchak The".