The "papada" is not strictly cheek, or jowl as it is called in America. The latter comes from the side of the head:

"Pork jowl is a fatty cut of meat along the side of the head"
http://www.foodista.com/food/DTMZM25R/pork-jowl

This part is called "careta" or "carrillera" in Spanish:

"Carrillera (cheeks):
The carrillera is formed from the muscles of the lower jaw, which are used for movement and chewing."
http://www.foodsfromspain.com/icex/cda/controller/pageSGT/0,...

The "papada" is a fatty piece under the mouth, extending down to the chest. It is what gives human beings a double chin:

"papada
1. f. Abultamiento carnoso que se forma debajo de la barba, o entre ella y el cuello.
2. f. Pliegue cutáneo que sobresale en el borde inferior del cuello de ciertos animales, y se extiende hasta el pecho."
http://buscon.rae.es/draeI/SrvltGUIBusUsual?TIPO_HTML=2&TIPO...

"PAPADA DE CERDO IBERICO
Parte grasa situada en la parte inferior de la cabeza debajo de la mandíbula, con corteza, de forma triangular, que va desde el morro inferior al principio de la paleta."
http://iberianmeat.com/productos/

This part is called the dewlap in English:

"However, there are also two pieces of meat, the secreto de papada (dewlap) and a cut from the belly (secreto de barriga), which are known as the “falso secreto” (false secret) as a result of their similar appearance and fat structure, although these are not as tender as the true secreto."
http://www.foodsfromspain.com/icex/cda/controller/pageSGT/0,...

"While there were delicious elements to follow, the meal stalled here. While I loved the beet “balloon” containing beetroot vinaigrette, I didn’t like either the texture or flavor of the pork dewlap (dewlap is the fold of skin hanging below the neck in many vertebrae species)."
http://thelovage.com/2011/carme-ruscalledas-sant-pau/

"The English translation for this mysterious meat spread is seasoned pork lard with cured pork added. And not just any cured pork, but pork dewlap, or the skin and meat below the hog's chin, pig wattle, if you will."
http://www.slashfood.com/tag/pork dewlap/

"Entrepà de vieira, caviar d’albergínia, dau de patata confitada i papada
Bocadillo de vieira, caviar de berenjena, taco de patata confitada y papada
Sandwich of scallop, aubergine caviar, “taco” of candied potato and pork dewlap 15,60 €"
http://www.restaurantethegarden.com/pdf/CartaTheGarden.pdf

"De monte", applied to meat, would normally imply "wild" (ie. roaming free), though it could mean "aromatic", ie. done with "hierbas del monte". But I think the idea is probably that this "papada" comes from "cerdos del monte", or wild pigs, so "wild pork" seems like the best bet. They could perhaps be called "mountain pork", and that might be a good choice if you want to make it "sea and mountain". "Monte" doesn't necessarily mean mountain, though, in fact in this context it probably refers to some sort of high wooded scrubland.

--------------------------------------------------
Note added at 3 hrs (2011-12-28 12:56:29 GMT)
--------------------------------------------------

The "monte" part is tricky. I do think it would normally imply free range -- pigs grazing in a "dehesa" -- rather than from a pig farm. However, something non-committal like "rustic", as Neil has suggested, might be safer. However, I do think this should be called "dewlap", which is what it is, not "cheeks" or "jowls" or "chaps", which all mean the same thing and are different. There are various cuts of head meat and they are not all the same: "papada" is a very specific thing.

--------------------------------------------------
Note added at 3 hrs (2011-12-28 13:15:25 GMT)
--------------------------------------------------

Here's a coincidence:

"‘Mar i muntanya’ with crispy pork dewlap, saffron ‘allioli’ and grilled squid."
http://www.bcnrestaurantes.com/eng/barcelona.asp?restaurante...