...
my $dir_path = "/my_dir";
my @dir = <$dir_path/*.*>;
if (@dir) {
  foreach (@dir) {
    next if -d; 
    my $temp_f_name = basename( $_ );
    # get just the file extension
    (my $file_extention = $temp_f_name)=~s/^([^_]+_)(.*)(\.\w{3,4})\z$/$3/eg;
        my $renamed_file ="oldsince_"."$file_extention";
        
        rename($temp_f_name, $renamed_file ) unless $temp_f_name eq $renamed_file or 
             warn "Couldn't rename: $!\n";
       }
    }
...