No, you are not flying to Reykjavik Iceland
When it comes to airlines nowadays misleading its customers seems to be the thing to do. Even when airports are way out in middle of nowhere airlines have a knack for giving these airports a fancy and inviting name.
This can be confusing at the best of times and downright horrible at the worst of times as unprepared people flying into, say Frankfurt Hahn, will testify. That particular airport could as well be called Luxembourg airport since it is mid-way between those two cities. After landing one still has to drive for an hour before reaching Frankfurt.
Much the same is the case in Iceland. A check by team Total Iceland shows that all the airlines flying regularly to Iceland mark their flights from xxx to Reykjavik. Even the local ones do even though you are not flying into Reykjavik city at all. All international flights land at Keflavik airport which lies about 40 to 50 minutes away from Reykjavik.
We know about people making the error of thinking a flight into Reykjavik is a flight into Reykjavik and since the airlines seem not to want to give people correct information we will.