Asked this week if the nickname might resurface in Arizona, Mathieu remained vague.
"I don't know if he's going to come back this fall," Mathieu told the Akron Beacon Journal at this week's NFL Rookie Symposium. "I really don't know. But right now, I'm happy being Tyrann. Tyrann is a fun guy, and I'm just ready to play some ball."
Mathieu saw plenty of snaps in offseason practices, and the defensive back is a likely bet to play a big role in nickel packages, with a chance to compete for the free safety job. When Cardinals coach Bruce Arians was asked if Mathieu could make an impact right away, he said point blank: "I don't think there's any doubt."
NFL.com's Ian Rapoport reported in May that Mathieu already has entered the NFL's drug-testing program after being kicked out of school and entering the 2013 NFL Draft waving a bright red flag. The Cardinals hope he can stay clean, no matter what he calls himself.
"I think it's going to take some time, just because 'Honey Badger' happened at such a bad time, a time where I wasn't making the best decisions," Mathieu said. "So going forward, if I'm able to make the right decisions, able to be that role model for the kids, I think the 'Honey Badger' can be a pretty positive person."
Follow Marc Sessler on Twitter @MarcSesslerNFL.