Dalvik - Dalvík is just a tiny town/village in that general area, not much bigger than other nearby towns, so Dalvík if not a fitting name.
[This area would more correctly be called 'Tröllaskagi'.
Saudarkrokur - Same as with Dalvík, a more fitting name would be Skagi, which is what the peninsula that extends out of the region is called. A more common name for that area is Skagafjörður, and it probably suits the region better though the borders are a bit different.
Hvammstangi - Húnavatn, Húnaþing, Húnaflói, one of these will do. Húnavatn is the name of the lake the area is always referred to, Húnaþing is the official name of the county, Húnaflói is the name of the bay off the shores of the region.
Bifröst - Should be called Holtavörðuheiði.
Vatnsfjörður - This is a tricky area, there is little basis for it in real life but I suggest either Reiphólsfjöll or Steingrímsfjarðarheiði.
Reiphólsfjöll are notable mountains in the area, Steingrímsfjarðarheiði is the area between the fjords it 'touches' on the north side and the fjords it 'touches' in the east side(about where the no. of armies lies).
Bolungarvik - Definitely Ísafjörður.
It's the biggest town of the Vestfirðir/West fjords and deserves the title more than Bolungarvik, which is rarely ever mentioned.
Drangsnes - Maybe Árnes, but there's not much distinction between these two in my mind.
Ólafsvík - Snæfell/Snæfellsnes. Preferrably the latter, if not excessively long.
Keflavík - Personally, I'd call this Reykjanes, but maybe it's more 'fun' having it Keflavík in case someone recognises the name from the U.S. Army base that used to be there. You decide, they're each as good to me.
Geysir - If this map was made for&by Icelanders this territory would be called Þingvellir, which is the name of perhaps the most historically important place for Icelanders.
But it isn't, so maybe Geysir is better as more people recognize it.
Snæfell - I guess if
you change Ólafsvík to Snæfell/Snæfellsnes it would be wise to change this as well, but I can't seem to find a fitting name for this territory.
The Lögur (lake), which is the 3rd largest lake in Iceland, is in this area, so you could name it after that.
Or not change either, that would work to. After all the names don't really matter that much.
Höfn - Djúpivogur.
Seyðisfjörður - The actual Seyðisfjörður isn't within that region's borders, I'd call this Héraðsflói.
Raufarhöfn - Melrakkaslétta is the name of the peninsula extending out of the region.
Húsavík - You could call this Mývatn, after the beautiful lake the region is best known for, and the northern part of the area is generally called Skjálfandi, but Húsavík is just as valid.
Reykjahlíð - Definitely Ódáðahraun. It's lava-covered ground + moss + some bushes for miles and miles. Definitely the most well known part of the region.
Oh, and one minor mistake, it's Vestmannaeyjar in one word, not Vestmannaey Jar
Ey is eyjar in plural.
Well we're very un-original when it comes to naming land-quarters as they're called here, you pretty much got it.
I don't think I can suggest any alternatives to any of these names
Well maybe you could call the East fjords 'Hérað', but I'm not sure though.
Anyways, sorry for being such a ... stickler, perfectionist, whatever. After all I'm probably the only one who'd notice