LAS CRUCES, NM—Advertising sales rep Brian Costello, 36, couldn’t say when or why, but he was pretty sure he’d heard the name “Herman Cain” at some point before.

LAS CRUCES, NM—Advertising sales rep Brian Costello, 36, couldn’t say when or why, but he was pretty sure he’d heard the name “Herman Cain” at some point before.