This Mckinsey article talks about brain-steering instead of brainstorming.
Basically, what it suggests is to have a focusses brainstorming rather than an open ended that leads you nowhere. You seek answers to the questions that you know or have prepared in advance. You do not throw open the questions to a big group, but spread the questions amongst smaller groups and then let them share their best ideas with the bigger group. It also suggests that you do not pick winning ideas in a hurry as the participants usually do not have a overall view of the problem and ideas need an executive level vetting.
Though I would avoid giving brainstorming a new name, but I agree with most of what the article says. To get the relevant answers you must ask the right questions.