Your 'pattern' is not being strored as a pattern but as a literal string.
So

my $newname=$Ren2Dol{$base};

is not doing a pattern match, but just a lookup

Then you would need to iterate through your patterns and reassign the name on success.

use strict;
use warnings;
my $string = '^a{4}b{2}';
my $patt = qr/$string/;
my %hsh = ($string => $string, $patt => $patt,);

my $test = 'aaaabb';

foreach (keys %hsh){
  print "YES for regex : $_\n" if $test =~ /$_/;
}
print "YES for existance : $_\n" if (exists$hsh{$test});
[download]

see qr// and perlre for how to compile a string into a pattern.

Hope this helps!