You may be thinking of Philip José Farmer's Dayworld trilogy, first published in 1985.
From the Goodreads link:
Dayworld leads a sf trilogy by Philip José Farmer set in a dystopian
future in which an overpopulated world allocates people only one day a
week. The other six days they're in suspended animation. The focus is
on Jeff Caird, a daybreaker living more than a day a week. He's not
like most daybreakers. He belongs to the radical Immer group working
to create a better government. Not all Immers are daybreakers, but
send information from one day to the next they've daybreakers like
Jeff. Immer daybreakers assume seven different personalities & jobs,
slipping from culture to culture in seven different worlds. While Jeff
& the other six go day to day, they run into problems while working as
Immer daybreakers. They must cover their tracks while trying to keep
up with seven different lives, families & jobs. It could drive a man
crazy. It does & the Immers must dispose of Jeff to keep the rest
safe. Jeff, wanting to live, tries to escape, but they have undercover
Immers in every job & government level. Jeff is caught & put in an
asylum, classified with multiple personality disorder. If considered
incurable he'll be killed. But Jeff has an escape plan.
The sequels are Dayworld Rebel, '87 & Dayworld Breakup, '90.