Perseverance has started to core the top of the 'Mount Meeker' target, its coring bit is placed a little to the left of the 'Dragons Egg' abrasion patch that the rover has been inspecting for several sols. For scale the diameter of the drill bit is ~25mm (1 inch). Processed F-L HazCam image from Sol 862 (July 25, 2023).
Credits: NASA/JPL-Caltech
I'm assuming whomever named these spots on Mars took inspiration from Mt Meeker in Colorado. This also has a rock feature on its southwest slope called the dragons egg.
The feature is prominent in a technical backcountry ski route called The Dragons egg couloir.
Basically they take a geological region from somewhere here on earth, such as Colorado or The Rocky Mountains, and take names from those regions.