The real origin of the term is a little fuzzy and there are two legends explaining the term, but one thing is sure and both legends share it: the term "Winchester" links back to the IBM 3340, an early storage system. In 1974 International Business Machines (IBM) introduced a storage subsystem for computer systems, or "Direct Access Storage Devices" (DASD) in IBM lingo. It's a blue box with a white top the size of a small refrigerator. Inside it has two mechanisms, one fixed and one removable on the topside inside the white upper part. Both storage units, the fixed and the removable, had a capacity of roughly 30 Megabytes.
The double 30MB capacity is what most people think lead to the system being nicknamed, or codenamed, the "Winchester drive". There's a rifle from well-known manufacturer Winchester that shoots .30-30 Winchester cartridges and was named the 30/30. Although the 30MB + 30MB capacity designation wasn't really accurate, it somehow stuck. According to IBM, it was development engineer Kenneth E. Haughton who coined the name.
The other, less military, and much simpler explanation for the "Winchester" nickname of IBM's 3340 is that it was manufactured at IBM's Winchester site. People inside IBM, as often in university or other large corporations, tend to refer to systems by the name of the person or workgroup that invented it or by where technology was assembled. Such designations are also very commonly found in NASA, large thinktanks or labs like XEROX PARC or general in research facilities.
The IBM 3340 used removable rigid disk modules where the read/write head assembly was fixed inside the module. This meant that when the magnetic medium was exchanged, the drive's read/write-head alignments remained perfect. No calibration or other treatment was neede when a module was changed. And although this made the module more expensive, it lead to a vast increase in possible capacity. No tolerance issues, no adjustments, no dust or particle contamination. Since then, drive mechanics where the platter and read/write meachnism is capsuled against environmental influences were nicknamed "Winchester drives" and Winchester has become synonymous with hard drive. But the term has lost popularity during the 1980s and 1990s years.
Looking at the actual technical specs of the IBM 3340, the 30/30 rifle link weakens, as the actual capacity of the removable modules wasn't 30 but 35MB. Also, higher capacity modules became available with 70MBs per spindle. IBM refered to the removable sealed cartridges as the IBM 3348 Data Module.