Daughterboard, shield, hat, cape, ...
The standard name for a subsidiary printed circuit board (PCB) that plugs into a main PCB is "daughterboard"
However, the somewhat artsy communities that produce these small experimental microcontroller boards each tend to invent their own name for daughterboards that have the required dimensions and connector to mate with the primary form of main PCB in that community
Raspberry pi: hat.
So they tend to borrow the name of some type of accoutrement that a human might loosely attach to themselves. There is a vaguely protective theme here but I think that is largely irrelevant.
I'm not sure what the first Arduino shield was but it was probably something that mediated between the Arduino and the outside world. Also from its shape it isn't too dissimilar to a rectangular shield, I suppose it also (uselessly) shields the Arduino from light (and fingers). Most Arduinos have no (or little) electrical protection on their inputs and outputs, at least some shields provide a modicum of additional protection - although that is usually not their main purpose.