I've got an actual hard copy phone book for my area of California, so I looked at the ads in the yellow pages. (I only skimmed through ads; I didn't look at every listing.)
I didn't find any "garages." The places that do mechanical work mostly described themselves as "auto repair" or "auto service." or even "auto repair service." They often had a phrase like that in the name (Ace Auto Repair or Acme Automotive). ,
Many body shops described themselves as "collision center" or "collision repair" although "body work" was also common. There were some places that had "body shop" or "auto body" in the name. (e.g. Joe's Body Shop or Ace Auto Body.) Mostly ones that have been around for a long time. One Body Shop opened in 1937.
A couple of body shops said they also do "mechanical repairs" but I found no mechanical places that advertised body work.