Having looked again, I think the trade term is e-collar. (Presumably short for elizabethan collar)Actually I took my cue from the word 'funnel' in the title of this thread, and so when I googled for pet funnels I found pet funnels; I looked around for a good reliable site that would tell me what the trade would call them, but didn't see anything obvious. If I'd searched for cones I would have found cones. 'Lampshade' makes the best sense to me, but can't really be the trade term, I suppose.
Ouch.And dogs in Elizabethan collars of course go 'ruff'.