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In fiction (which takes place in a universe much neater than our own), a change of name almost always indicates a change of status. Thus when Strider becomes Aragorn his status changes from vagabon...
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#4: Attribution notice removed
Source: https://writers.stackexchange.com/a/25524 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/25524 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
In fiction (which takes place in a universe much neater than our own), a change of name almost always indicates a change of status. Thus when Strider becomes Aragorn his status changes from vagabond to king. How a character responds to the change of name, therefore, is a signal of how they respond to the change of status. Failure to change would indicate either a refusal to acknowledge the change of status or a claim to an intimacy that supersedes those of status, like members of the royal family calling the queen Lillibet or Grandma, or a claim to superior status that does not require you to acknowledge the new status. So how your characters handle the new name indicates whether or not, and in what way, they acknowledge and accept the character's new status.