Is it fat, skin, muscle or chin position?
Almost everything that decides whether a patient is satisfied is settled before the operation, during the assessment. Fullness beneath the chin can come from fat lying under the skin, loose or thin skin, visible platysma muscle bands, a recessed chin, or deeper structures beneath the neck muscles. Liposuction treats only the first.
This matters financially. If the surgeon removes fat from skin that cannot contract, the neck can look looser afterwards, and the usual remedy is a neck lift, which is a larger and costlier operation. If a recessed chin is part of the picture, adding chin augmentation may serve you better than more suction.
A clinic that examines your skin, muscle and profile before naming a price is doing the work that protects your money. A quote offered from a photograph alone is a starting estimate, not a plan.