There are no rules for naming cartridges. The inventor can call it anything they want.
Pretty much...
however, there are some more or less standard conventions that are usually followed. One is that the number in the cartridge name have some relationship to the caliber of the bore, but need not be the exact diameter or the bullet used.
In the early days of pistol rounds, (revolvers are pistols, too..
) the .38s were actually .38 caliber bullets. Rounds were loaded with heel type bullets (like .22LR still is today) where the widest part of the bullet is the same diameter as the case, and there is a smaller diameter "heel" of the bullet inside the case. When this changed to inside lubricated bullets the widest part of the bullet was inside the case, and of course, in order to fit, a smaller diameter. With the lead bullets of the time, the smaller diameter of the "new" bullets didn't matter much, as the lead would upset in the bore and seal well enough for accuracy.
Over time, the actual bore diameter dimensions were reduced to match the bullets, but the original caliber names were kept. Which is why .38s are actually shooting .36 (.358"" diameter bullets.
Another convention is using bore diameter measurements (not bullet diameter) in the cartridge name. All the common .300s and .308s use the same diameter bullets (.308) just .300s are named for the land to land bore diameter, while .308 is the measurement groove to groove.
As to something like the .275 Rigby, its the English measurement of 7mm (.284") minus groove diameter, changed from the actual .276" measurement for market appeal (.275 was thought to be more appealing to the buying public than .276)
Another convention is using a name that includes the parent case, such as 7mm-08 (a 7mm bullet in a necked down .308Win case) or .22-250 (a .22 made from the .250 Savage case).
However, on the other side of the pond, they do it just the opposite way, putting the parent case name first. .577/450 Martini, .450/400 Jefferries, etc.
There are other "rules" that are generally followed, and then there are a host of exceptions.