Not all A-10s get nose art, but for the ones that do, paint crews refer to the different paint schemes by most prominent feature, the teeth.
The interesting video in this post features crews assigned to the 576th Aircraft Maintenance Squadron (AMXS) at Hill Air Force Base (AFB) painting three variations of nose art on A-10 Thunderbolt II aircraft that went to the Ogden Air Logistics Complex for depot repairs, modifications and maintenance.
Not all A-10s get nose art, but for the ones that do, paint crews refer to the different paint schemes by most prominent feature, the teeth.

The application of nose art is the last step in maintenance before the aircraft is delivered to flight test and back to the unit.
Towards the end of the last year, the 576th AMXS started to upgrade its traditional manual media blast paint removal process by using new-generation robots to strip the paint from A-10s that come to Hill for depot overhaul and maintenance.

Robotic media blasting used to strip paint from fighter aircraft such as the F-16 Fighting Falcon has been around at Hill for more than three decades. The technology has been used for the first time to remove paint from the A-10 Thunderbolt II on Dec. 4, 2019.
This process reduces man hours it takes to strip paint from the aircraft, increase safety by removing employees from the blasting atmosphere, and result in measurable time and costs savings.
The paint removal process is accomplished by two robots, each with four hose attachments that move independently along both sides of the aircraft. In addition, the time to strip an A-10 is decreased from three days to 9-12 hours.
Video: R. Nial Bradshaw / U.S. Air Force