Correcting the double chin is within the domain of a board certified plastic surgeon, and a member of the American society of Aesthetic Plastic Surgery.
They are the only surgeons qualified and trained to deal with all aspects of the double chin. This could be liposuction , in some cases the fat is under the platysma muscle then that has to be removed, sometimes it is the combination of these procedures.
Correcting a double chin is the per view of the surgeon who specializes in facial rejuvenation, as the neck is generally considered part of the face. The easiest way to identify someone is to use this site and look to see if facial rejuvenation is one of their specialties.