I was bored and came up with provincial names for Hammerfell, if it had provinces. I used the suffix -iyah found in some Arabic place names:
Alik'riyah - Alik'r Deaert area
Shiraziyah - Cape Shira on the western coast of Hammerfell
Gilaniyah - Khefrem's Boot and Gilane
Bangkuriyah - Bangkorai
Craglurniyah - Craglorn
Suq al-Tijarah - the area dominated by the Caravan Trading company in Skavyn. The words come from "Suq" and "Tijara" which means "market" and "trade" respectively in Google Arabic. This region was going to be called "Sunforge" for ESO.
Al'ahzan - The area that was going to be "The Weeping Desert" for ESO, east of Taneth and Rihad. It comes from the word meaning "The Sorrows" in Google Arabic.
Tanethiyah - area around Taneth
Rihadiyah - area around Rihad
Goldmoor has been mentioned as a region in a book, but its location was never revealed, so I left that one out.