Display identification
Display identification is how BetterDisplay recognizes a display and finds its saved preferences. Depending on the chosen strategy, it can use a macOS UUID, vendor/model/serial information, names, connection-location details or EDID data.
A UUID is an identifier supplied by the system. It is not the same as the serial number printed on the monitor. Two identical monitors can expose very similar identifying information, and one physical monitor can receive a different system identity after a connection or installation change.
This distinction helps explain why imported settings sometimes need to be transferred to a newly recognized display. A custom name makes the display easier for you to recognize, but it is primarily a readable label, not proof that the app has found a particular physical monitor.
See EDID for the display-supplied information and Additional Settings for identification preferences.