What is the name of the small pins that are used with small wheels / rims?
LEGO and others sometimes calls those pieces a "bearing element". This term however is not limited to just that axle.

LEGO's replacement parts service calls the holes they go into "HOLE Ø11" (possibly read "Hole Diameter 11"):



The width of the axle is roughly equivalent to the width of a "bar", like the 30374 piece used for Lightsabers as such.

None of these names are particularly satisfactory, but I'm not aware of any better names.