Truly sorry if this has been mentioned/asked:

I know from Fallout 3 you could change the gear on your companions, is this not possible in New Vegas?

I can't get that stupid looking Druid hood off of Veronica.

If you happen to be on PC, http://www.newvegasnexus.com/downloads/file.php?id=34757.

It's possible on PC via mods. Barring that, no such luck.

sort of.
If you give armour or stuff to the companion they often equip it. same goes for weapons.

They always seems to choose gear with highest damage threshold. If its equal, they do not bother changing.

On PC, simple:
open console
click on Veronica
type "prid (Veronica's id number shown in middle top of the screen)"
type "inv"
look for "Veronica's robe hood" in the list (if it doesn't show, empty her inventory)
type "removeitem (the hood's id) 1"

On console, giving another headgear should cause her to switch to it, but i don't think it's possible to get her bare-headed.

Edit: actually, that "prid" part is not necessary.

Veronica equips it but leaves the silly hood on.