The original Intel 8086, 80186, and 80286 were 16-bit processors. However, the 80386 aka i386 was the first 32-bit processor in the x86 line.
The most logical name to refer to the 32-bit x86 architecture is x86_32, since it's the 32-bit extension of the x86 architecture, and it matches the style of the x86_64 name which is the 64-bit extension of the x86 architecture.
The name x86 is a retronym. Intel did not give a name to their instruction set initially. They later gave it the name IA-32, adding to the confusion. Before an official name was given, different groups came up with different names.
Microsoft decided to call x86_32 as x86, and x86_64 as x64. Microsoft's naming is why you're used to seeing x86 refer to 32-bit x86.
Linux distros decided to call x86_32 as i386 after the first x86 chip that was 32-bit, and then they called x86_64 as amd64 after the first x86_64 chips that came from AMD to avoid confusion with Intel's competing IA-64 (Itanium) architecture.
Apple decided to call x86_32 as i386 similarly to Linux distros, and then they called x86_64 as the logical name x86_64.