spent tent
n. A room designated or set up for napping, particularly at a workplace.
So companies opened nap rooms, encouraging workers to take 15- to 30-minute breaks to recharge.

An architectural firm in Kansas City created "spent tents," complete with sleeping bags and CD players, to slide into when you're spent.
—Susan Ager, “Yes, an on-the-job snooze just might work,” Detroit Free Press, December 14, 2000
One of the nation's largest architectural firms, for example, Kansas City-based Gould Evans Goodman Associates, offers three "spent tents" furnished with pillows, blankets and alarm clocks for employees who work long hours when project deadlines loom. "It's out of the way, so you don't feel guilty," said napper and architect Greg Nook, 44.
—Usha Lee McFarling, “Firms Make Nap Judgment,” San Jose Mercury News (California), September 30, 1998
1998 (earliest)
At the huge Gould Evans Good architectural business in Kansas City, Missouri, stressed-out executives are encouraged to visit the "Spent Tent", where they are provided with clean sheets, a pillow, an alarm clock — and a German shepherd dog called Ginger to pat.
—Allan Hall, “Fido leads fight for less stress,” The Evening Standard (London), May 13, 1998
Is workplace napping becoming accepted in the hard-charging North American business world? I'll believe when I see it, but if the number of new words related to napping on the job are any indication, there's at least a pro-nap faction out there. Besides spent tent there's nap room, solitude nook, wellness room, and the very cozy-sounding nap nook. Of course, those of us lucky enough to work at home have a built-in spent tent: the couch!