This has been primarily a branding/donation exercise for business schools, emulating the Wharton brand.
Almost every business school (good, bad, indifferent) has a name. Fuqua, Tuck, Kellogg, Kelley, Mendoza, McDonough, McCombs, Stern, etc… It is pretty meaningless since everyone does it. Anyone really care about the Jack Welch School of Business or the Wayne Huzienga School of Business?
At some schools, they even have separate names for their undergrad and grad B-schools. Like McIntyre and Darden at Virginia.
Harvard, Columbia, Stanford get along just fine without separate b-school names.