The memory efficiency you should be concerned about is "how can I best remember or figure out how this code works". When computers, even the one in your pocket that you call a phone, have multiple gigabytes of memory, shaving a few bytes here and there is almost always a waste of time.

Consider instead how easy it is to understand the intent of the code, how robust the code is against programming errors, and how easy it will be to maintain the code in the future. In all of those cases a named function is a big win because the name can (and should) convey intent.

I'm unsure what you mean by a "local subroutine" as all named subroutines in Perl are scoped within the current package. Nesting subroutines makes no difference to their availability to other code.