The first documented use of the name mixed martial arts was in a review of UFC 1 by television critic Howard Rosenberg, in 1993.[6] The term gained popularity when the website, then one of the biggest covering the sport, hosted and reprinted the article. The first use of the term by a promotion was in September 1995 by Rick Blume, president and CEO of Battlecade Extreme Fighting, just after UFC 7.[27] UFC official Jeff Blatnick was responsible for the Ultimate Fighting Championship officially adopting the name mixed martial arts. Previously marketed as “Ultimate Fighting” and “No Holds Barred (NHB)”, Blatnick and John McCarthy proposed the name ‘MMA’ at the UFC 17 rules meeting in response to increased public criticism.[28] The question on who actually coined the name is a question still in debate.[8]

This information, and more about Mixed Martial Arts (MMA), can be found at the following Wikipedia link;