That won't work under use strict;, and for very good reasons: How can I use a variable as a variable name? and Why it's stupid to `use a variable as a variable name'.

If you really needed this type of functionality, you could use hashes of arrays instead, see e.g. perldsc along with perlreftut and perlref.

use warnings;
use strict;

my %data;

my $string = "awesome_array";
my $other_string = "another_awesome_array";

push @{$data{$string}}, 1, 2, 3, 4, 5;

foreach my $element (@{$data{awesome_array}}) {
    print "$element\n";
    push @{$data{$other_string}}, $element;
}

print @{$data{another_awesome_array}};
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