Some people will cook Chicken Necks and clean the meat off of them for soup or for the dogs.
To do this though, you must have the patience to be absolutely thorough about looking for the teensiest of bones, and you can't let your mind wander. You must pay attention, otherwise, the risk of letting bones get through your hands and into your small pile of meat is too great.
There are certainly times in history when economies such as picking the meat off from Chicken Necks is to be lauded. Many of those who grew up during the Depression or wartime still do it. But while many people are hyper conscience about food nutrition -- as in, does this have an extra gram of fat that is going to kill them when they're 97 -- others are more old-fashioned in regard to food safety, and bones, which will kill someone right now, are right up there on the list.
Some people just discard Chicken Necks entirely. This is equally the wrong approach. They can be used to make an exceptionally flavourful stock from.
Chicken Necks can be roasted right in the pan with the bird, making sure they sure they are whole. Or, they can be roasted separately in an inch or two (3 to 6 cm) of water. When the water is gone, add some more, cook a bit more, then pour that water off into the pot in which you will eventually make the gravy. Then deglaze the pan you roasted the neck in and add that deglazing liquid to the gravy pot. Discard the necks afterward.
You can also just boil the neck in a separate pot of water, then discard the neck and use that stock for your gravy. Strain the stock through a very fine sieve first before using.