This is a jukugo word, which usually means on'yomi readings from the kanji (except for 名 and 屋, which are kun'yomi here). If you know the readings of your kanji you'll know how to read this as well. For な just think to 名前 (なまえ) which uses the な reading. The "name" (名前) of this city is what? It's Nagoya. Watch out for rendaku changing こ to ご too.
Nagoya has a lot of delicious food.
I had work in Nagoya today again.
When I visited my friend in Nagoya, I was treated to a delicious pork cutlet called yabaton.