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@pkw here we run into the whole Let Over Lambda paradigm of having your function-lambda-expression -s (which can be closures) include their own machinery for their use and implication changing over time.
I guess in this case interactive renaming could be like
(setf (symbol-function 'new-name) (symbol-function 'old-name))
(fmakunbound 'old-name) (unintern 'old-name)

(though the lambda could also just sit in the symbol-value to be funcalled or applyed as well)