Have you tried? You need some extra braces in there, and need to drop the second my, but other than that your code works...

my @names = qw(A B C D);
for (my $i=0; $i<4; $i++) {
   @{$names[$i]} = $i;
}

use Data::Dumper;
print Dumper(\@A, \@B, \@C, \@D);
[download]

These are called symbolic references. It is forbidden by the strict parameter because it's usually a bad idea. That's not to say it's always a bad idea; strict refs is just about the only part of strict that's occasionally worth disabling (occasionally, in a small lexical scope).

There are usually better ways of doing it. Here's one way, using a hash of arrays:

use strict;

my %ARRAYS;
my @names = qw(A B C D);
for (my $i=0; $i<4; $i++) {
   @{ $ARRAYS{$names[$i]} } = $i;
}

use Data::Dumper;
print Dumper(@ARRAYS{@names});
[download]

Here's another way using hard references instead of symbolic references:

use strict;

my (@A, @B, @C, @D);
my @names = (\@A, \@B, \@C, \@D);
for (my $i=0; $i<4; $i++) {
   @{$names[$i]} = $i;
}

use Data::Dumper;
print Dumper(\@A, \@B, \@C, \@D);
[download]