What you are trying to do is called "symbolic referencing" and is generally considerd to be a bad thing. Instead, you should probably create a hash that uses your names as keys. This avoids various scoping issues, and keeps them all in a set so its easier to deal with them as a group. Perhaps you want something like this:

#!/usr/bin/perl -wT
use strict;

my @arr_name = (10,11,12,13);

my %hash;
for my $d (1..@arr_name) {
  my @newarr = ($d..5);                # example data
  $hash{"new_arr_$d"} = \@newarr;      # a new array containing new da
+ta
                                       # with the name "new_arr_$d"
}


for my $key (keys %hash) {
  print "$key => ", join(',', @{$hash{$key}}), "\n";
}

=OUTPUT
new_arr_3 => 3,4,5
new_arr_4 => 4,5
new_arr_1 => 1,2,3,4,5
new_arr_2 => 2,3,4,5
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-Blake