Who's This? No, not the sexist 1960s ad executives, the colorful villains from Who's Who Update '87 #4, page 4.
How you could have heard of them: From Hawk & Dove #18-19 (1990), Farley Fleeter, the leader of the Madmen, gained the ability to turn people into Madmen with his touch thanks to a pharmaceutical incident. That allowed the Madmen to appear fairly frequently as canon fodder (habitually shot down by heroes and villains alike), appearing in such books as Justice Society of America, Manhunter, Nightwing, Infinite Crisis, Blue Beetle (2006 Jamie series), and others.
Example story: Blue Beetle #3 (Charlton series, 1967) "The Madmen" by Steve Ditko and David Glanzman
Those were simpler days, and the Madmen were perfectly suited to them.
Who's Next? All I can say is that I took your suggestions from last week into account!