As I understand it, creating a new livery creates a new airframe, as each livery gets it's own unique .ini file, which stores relevant info for that airframe.
This from the manual regarding the Liveries concept:
Instructions for Painters
Those who want to create liveries for DC3, should have a few things in mind.
We will provide you a paintkit, for both Photoshop and Substance Painter.
Each livery requires a .ini file for data and information to be stored. We will provide you with a file that you can edit it.
The liveries' .ini files are located in the X-Plane 12/Output/DC3 folder.
The file for your livery should be named exactly as the livery folder. For example is the livery folder is named United Airlines, the file should have the name United Airlines.ini.
If you load DC-3 in X-Plane, with your livery folder in place, and without creating or adding the required .ini file, will create one for you, replicated the default's livery one. Then you can edit this file.