I believe you're asking to convert the month number (zero based) into a month name, and store that name in the variable where the number had previously resided.

use strict;
use warnings;

my ( $day, $month, $year ) = ( localtime )[3,4,5];
$month = (
  qw/ January   February  March
      April     May       June
      July      August    September
      October   November  December  /
)[$month];

print $month, "\n";
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The constraint on not using any module or intermediary variables is a little odd. It's a small enough problem (assuming this is the entirety of the problem) that a module wouldn't make much sense. But the requirement to store the result in the original variable without any intermediate variable, while not hard to accomplish, reads like an interview or test question.

If you don't need to store the day and year, you could even get away with a one-liner, and no variables at all:

perl -e 'print +(qw/January February March April May June July August 
+September October November December/)[(localtime)[4]],$/;'
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Not very useful though. ;)