The Hanger Rack in Animal Crossing: New Horizons doesn’t point to one famous branded object, but it does tap into a small slice of 20th-century design history.
Freestanding clothing racks became common in the early–mid 1900s as urban apartments got smaller and closets weren’t always built in. Department stores and garment factories also relied on simple metal pipe racks to move and display clothing efficiently. That industrial look — exposed bars, minimal frame, purely functional — later became part of the modernist and loft aesthetic, where visible storage is intentional rather than hidden.
In other words, the Hanger Rack reflects a shift in how we think about storage: From furniture that hides clothing (armoires, wardrobes) to open, utilitarian racks that display it.
The “utility” goes much further beyond display, of course. With hanger racks you have much easier access to clothes and if you use it as a drying rack, you can save wear and tear on your clothes while getting a “free humidifier” for your room, something that’s been particularly useful to me this dry winter.
This MULIG clothes rack from IKEA is a dead ringer for the Hanger Rack in ACNH, and best thing about it, at under $10 (as of this writing), it's very much affordable (some Amazon sellers charge upwards of $300 for essentially the same amount of metal and plastic).