Well the 7x57 or7mm Mauser or .275 Mauser ...

Rigby historically have been smart labelling their rifles:
"Rigby .275 bore".

Gunwriters picked it up. It has become part of general popular usage.

The association with Rigby is probably due to in English speaking countries the popularity of .275 rifles and the chamerbing by Rigby.

At one time, still? Gunwriters blab the 7x57 is a dead cartridge. So unpopular it no longer exists. I remember reading an article where the writer discussed how the 7x57 loaded ammo was unpowered. Due to 7x57 loaded ammo needing to cope with older rifles not capable of modern pressures. Some military rolling block single shots or some such.

The 7mm/08 is a dead cartridge, not the 7x57. The7mm/08 was the must have creedmoor of the day.

Accidentally the .275 Rigby nomenclature is accidentally sort of like many modern words where the originally meanings have been completely changed on purpose. And 99% of people parrot these words with the new meanings.

Btw I always preferred the nomenclature 7x57 and perhaps 7mm Mauser. The ".275 Rigby" always sounded affected.

Not that I wouldn't mind a vintage Rigby, WR, Jeffery or H&H .275 bore classic sporter.