Why is it Called Jimmy Greens?

From Metromix:

Jimmy Green’s
The place: A South Loop sports bar dedicated to Chicago teams and serving bar food and more than 50 beers.
So who's Jimmy? Jimmy Green’s was an old-time tavern on Taylor Street in Little Italy where a lot of locals used to hang out.
The history: “When a bunch of guys from Taylor Street are opening a place in the South Loop, what better name could we choose?” says co-owner Jeff Terrana.
Jimmy’s dish: Terrana thinks Jimmy, the owner of the now-gone Jimmy Green’s, likely was a man of simple tastes. “He’d probably order either a pizza and a beer, or a burger and a beer, or maybe an Italian beef sandwich, one of our specialties. And a beer.”