Flybe might be referring to it as Reykjavik but from what I've been reading they're actually operating to/from Keflavik which is a totally different airport and 50km from Reykjavik!
If so then they might at least be honest and refer to it as "Reykjavík-Keflavík" so passengers actually know which airport they're travelling to/from
Take your point, but the same could be said about Arlanda (40km or so from Stockholm) and Stansted (50km plus from London).
As a matter of interest, do any international flights operate to REK these days?
Makes BHX approx 10km from the city look brilliant!!!