Oh. They did.
"On January 24, 2013, the franchise announced it would rename itself the Pelicans, effective after the conclusion of the 2012–13 season. The Charlotte Hornets' name, history, and records from 1988 to 2002 were returned to its original city to be used by the then Charlotte Bobcats franchise, which subsequently became the Charlotte Hornets, starting May 20, 2014."
Given how the Browns/Ravens are handled here, I'd say it'd be best to the Pelicans as the newest team. The date could be 2003 (when records begin), or 2013 (when they officially were rebranded).
Even if they don't get featured, their takes are still significant, our non-featured quizzes have been taken 21,057 times, without which we would only be at rank #131.
It's also important to make the quizzes aesthetically pleasing, and to treat them like art.