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According to the original description (Regan, 1906), the type specimens of Heterogramma borellii were collected by "A. borelli". I don't really know who he was. In Latin, masculine possessive/genitive words end in 'i'. If the name ends in 'i', then a double 'i' is used.
Steindachner (1875) named the species "Geophagus (Mesops) agassizii" in honor of Louis S. B. Agassiz, leader of the Thayer Expedition (1865-6), who collected some of the type material in the Lago Maximo. I have no idea why Steindachner added 'ii' when only 1 'i' would be correct. Because the original name has 'ii', then this is the spelling used.
Kullander (1980) named A. elizabethae after Elizabeth Agassiz, wife of Louis, who accompanied her husband on the expedition. Since it was named for a lady, it uses the Latin feminine possessive/genitive suffix, 'ae'.