One of the most popular gifts this Christmas will be the $600 Dyson Airwrap, a hairdryer-meets-styling tool that upended the beauty industry when it was launched five years ago.

But now that it’s facing a raft of competitors, perhaps the Airwrap isn’t quite as hot as it was. To stay atop the wish lists, James Dyson, founder of the eponymous company, must follow in the footsteps of fellow billionaire Bernard Arnault, who controls LVMH, and reinvent Dyson as a luxury brand.