I wouldn't say so; "halsen" means "the throat", and "nakken" means "the neck". https://en.wikipedia.org/wiki/Throat https://www.sundhed.dk/borger/sygdomme-a-aa/oere-naese-hals/om-oere-naese-og-hals/halsen/
Ok this might help clarify things, as I was confused too, but if you look at the hover prompts it gives the meaning of nakken as "back of the neck", so when talking about the back of the neck it's nakken. Coincidentally when I tried to translate the sentence, You turned red in your neck, with google translate, it used hal instead of nakke. So perhaps hal is used at times to refer to the neck, when it pertains to the front of it? Not sure, as I'm not a native Dane.