In the May 1985 Word Ways, Dmitri Borgmann defined as isogram (actually, he recommended "asogram") as a verbal entity in which each each of the alphabetic letters used appears an equal number of times. He further defined a solo isogram as an isogram in which said equal number was one (CAT), a pair isogram when the number was two (DODO),and a trio isogram when the number was three (CHA-CHA-CHA).
"Isograms: The Sequel,"
Word Ways: Vol. 31
, Article 17.
Available at: https://digitalcommons.butler.edu/wordways/vol31/iss1/17