I totally agree that the “name=Windsock” is probably incorrect; it is, regrettably, a quite common error. I have removed handsfull of “name=hangar”, “name=control tower” and more such from aerodromes all over Europe. Even worse was the chap who added “icao=LFxx” to lots of windsocks and control towers in France.
What I would find acceptable, and sometimes apply, is a “description=” but for a windsock that would add no value since there already is an “aeroway=windsock”.

And no, the standard renderer does not honour the “aeroway=windsock”, it is very poor at rendering aerodromes anyway. I am developping a python script that does use the information, but it is far from being good enough for publication.