There's no other name for it. That's the definition of a double spend.
I think a double spend, in theory, is when you send the same money to two people and neither is reversed. This should be impossible with bitcoin. What happened was a blockchain fork and one of the spends was reversed when the older fork became the "true" fork.
So I agree that this is not a double spend.
Say I buy something from you and pay with
BTC. The transaction gets six confirmations and then you send me the item I bought. Then, the transaction gets reversed because the fork and I get the
BTC back. You lost the item and the Bitcoins and now I'm able to spend them again.
The transaction was reversed, but the merchant lost an item due to a network error, he didn't anything wrong. Call it as you want, but
effectivelly it is a double spend.