Stampings on the barrel regarding caliber designations were less a matter of patent rights and more a matter of company pride.
If your main competitor in the field developed a cartridge that was quickly becoming the defacto standard, would you want to admit defeat and stamp it on the side of your company's guns?
No.
Actually, cartridge names weren't patented at all. A patent denotes a technology, while a copyright or a trademark denotes something's name.
Over the years, Colt was particularly badly stung by Smith & Wesson's success at developing cartridges that became FAR better sellers than Colt's counterparts.
A few exampes are the .32 S&W, the .32 Long, the .38 S&W, the .38 Special, and the .357 Magnum.
Colt had the .32 Short Colt, the .32 Long Colt, the .38 Short Colt, and the .38 Long Colt. With the exception of the .32 Short Colt, which was a decent seller, S&W's cartridges handily outsold Colt's to the point where Colt finally had to counter the success by adopting S&W cartridges, but renaming them in the process.
They renamed the .32 S&W Long the .32 Colt New Police; the .38 S&W becamse the .38 New Police/Super Police (different bullets); the .38 S&W Special became the .38 Colt Special or simply the .38 Special; and the .357 S&W Magnum became the .357 Magnum.
As far as the .357 Magnum, I don't really know how Colt got away with stamping just that on several hundred pre-WW II Colt New Service revolvers because in 1935 Smith & Wesson had trademarked the term Magnum as it applied to handgun cartridges.
About the only revolver cartridges that Colt developed that really kicked ass in the market place were the .41 Long Colt and the .45 Colt, neither of which really had an S&W counterpart. Yes, S&W had the .45 Schofield, and it could be used in either the S&W or Colt revolvers, but S&W brought it out as an expediency measure when it was trying to sell handguns to the Army. The .45 Colt was too long to fit the Schofield's frame.
Other companies engaged in this renaming process as well, particularly Marlin when it came to chambing Winchester rounds.
That kind of company rivalry is still seen occasionally.