Vertical Chin Lengthening
If you are not concerned about your bite (meaning going for orthodontics with jaw advancement surgery) then a vertical lengthening genioplasty or a vertically lengthening chin implant can be done. The key decision between these two are the change in horizontal projection if needed. Since you want horizontal chin projection as well the vertical lengthening implant and bony genioplasty are both options for consideration.
you would need to have an xray taken to see if there is a jaw issue. From this picture, I would suggest jaw surgery rather than chin.