I am currently in the process of selling a doo-dah on ebay.

No, this isn't an ad, but if you want to have a look :.)))

It's a sort of swivelling arm thing (same sort of mechanism as
a desktop lamp) which attaches to a dust/fume extraction
system so that it can be manouvred over where you're working.
The problem is, I don't know what it's called.

Does this sort of fitting have an industry name?

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Big Egg
Visit my ebay shop for welding and tools and stuff:
http://www.stores.ebay.co.uk/honyaservices