It is sometimes referred to as "jowls", or, when it is particularly pronounced, a "double-chin". As excessive skin in this area is sometimes a sign of being overweight, having jowls is not usually desirable, but the latter expression "double-chin" is considered particularly insulting.
For non-overweight persons, this area of the body is not normally pronounced, and there isn't a particular general name for it. Looking at some medical charts, it may be the "submandibular triangle", but this is not in general use. As far as most non-medically trained people are concerned, the chin ends where the neck begins. If you wanted to specify that area as opposed to the most pronounced part of the chin (the mandible) you would perhaps say "under the chin".