The camera model is the product name stored in the EXIF Model tag (0x0110), an ASCII string in IFD0 right after Make. It identifies the kind of device, not the unit in your hands. That job belongs to the serial number.
Vendors disagree on what goes in it. Canon repeats the brand (Canon EOS RP), and so does Nikon (NIKON D850). Sony uses its internal code, so an a7 III shows up as ILCE-7M3. Apple writes the marketing name, iPhone 15 Pro, and Samsung writes a model number starting with SM- that you have to look up. Viewers that glue Make and Model together therefore print "Canon Canon EOS RP". The file is fine; the two fields simply overlap.
The camera model is stored twice
Canon and Sony (SonyModelID), among others, also record the model a second time inside the maker notes. On a Canon EOS RP JPEG:
$ exiftool -a -G1 -s -Model -CanonModelID -CanonImageType photo.jpg
[IFD0] Model : Canon EOS RP
[Canon] CanonModelID : EOS RP
[Canon] CanonImageType : Canon EOS RP
$ exiftool -a -G1 -s -n -Model -CanonModelID photo.jpg
[IFD0] Model : Canon EOS RP
[Canon] CanonModelID : 2147484723CanonModelID is a number (0x80000433) that ExifTool maps to a name. Editing Model leaves it alone, so a file whose Model says one thing and whose maker notes say another has obviously been touched. If you change Model to hide the camera, strip the maker notes too.
Phones, privacy and fingerprinting
On its own, a model name is weak evidence: millions of people own the same phone. Combined with the OS version in Software and the lens string, it narrows things down a lot more than people expect. Clean photos before posting them anywhere you mean to stay anonymous.
iPhone photos are usually HEIC, which our tools don't accept; to check them on the phone, see viewing photo metadata on iPhone. For JPEG and TIFF, the EXIF editor can rewrite Model (128 characters max, no commas or colons). With ExifTool:
exiftool -Model="Canon EOS R6" photo.jpg
exiftool -Model= photo.jpg