I don't know based on the rulebook.

The rulebook context on page 6 explains that the text "You may treat this card as having the same name as any specific character" allows you to change the name of the card to another character’s name, and that all other aspects of the card stay the same. However, it does not specify whether you can change the name multiple times in a turn or only once. There are no timing or frequency restrictions provided in the context.

To answer this question definitively, the rulebook would need to clarify whether this ability can be used repeatedly or only once per turn or per game.

Source: Core Rulebook (pp. 1, 4, 5, 6)