The episode Say My Name contains one of the most iconic scenes in Breaking Bad, wherein Walter demands that the gangster "say [his] name" upon realizing who he is. This is significant because Heisenberg is a mysterious, almost legendary, figure that few people have seen, but who has quite the lore following him.
Which other characters in Breaking Bad specifically knew that Walter White was Heisenberg, not just simply "involved with either drugs or criminal activity"?
Expanding the list in bizentass's comment (started as a comment of my own but then it got long):
Walt first used the name Heisenberg when he met Tuco. A few members of Tuco's gang were there to hear it. Badger and Skinny Pete know. Combo knew. Badger's cousin Clovis (the guy who ran the junkyard where they stashed the RV for a while - remember Walt ran up to tell them they had to get rid of the RV and Badger explained: "he's Heisenberg").
Skyler might have put it together at some point from knowing a little bit about Walt's business and hearing Hank talk about the hunt for Heisenberg, even though Walt kept her out of the loop as much as possible. I can't remember whether the name was used at the family dinner where Walt told everyone that Gale wasn't the "meth chef". If she didn't hear it then, I'm sure she did at some point before Hank figured it out.
Other maybes: in Saul's little group, his secretary seemed to know a lot, and his "A team" Kuby and Hewell. Todd, Uncle Jack and his gang. Lydia. All of them were involved in Walt's business when he was using the name. I don't remember if they ever heard or used the name on-screen.
He didn't use the name much (maybe not at all?) during the period when he was working for Gus. (Heisenberg isn't an employee. Heisenberg is the boss.) So Gus's other employees like Gale, Tyrus (the guy who replaced Victor), and Dennis (the guy who ran the laundry) may not have heard it. But they might have heard of the Heisenberg brand as a competing product before he came to work at the laundry, and it wouldn't have been hard to figure out.
Then toward the end, after Hank's realization, the list quickly grew to include Marie, and Steve Gomez, and then it was public knowledge (Heisenberg graffiti on the wall in his house).
Walter had introduced himself as Heisenberg to a number of drug dealers right from the first season. After Gustavo Fring's murder, his notoriety would have soared. Declane might have had trouble putting a face to Heisenberg but the product, Walter's speech and Mike's nod would have made things clear for him.
