I can't quite make out the manufacturer name though it may be Hilton but they are "American Made" bits. I think only a couple of the bits in the case are original.
Perhaps the name is "Fulton."
Are any of the bits marked with a name?
I can only imagine that this type of case was probably obsolete by the 1950s.
Starrett may still have those cases for their pin punches. I know they did 10-15 years ago.
Sadly, the Starrett punch storage boxes are now made of injection-molded plastic instead of wood. Still the same style, but not the same aesthetics.
Turned wooden storage boxes like that were common until fairly recently as larry_g said. Starrett offered them for their pin punch sets and also for their center punch sets, as did most other now-defunct precision tool manufacturers (Millers Falls, Lufkin, etc.)
Square and rectangular wooden storage boxes were also common for sets of larger punches, and for figure and letter punches (and some can still be found that way, but others are now in plastic boxes).
