Use a hash of arrays:

my %arrays = (
  FOO => [1,2,3,4],
  BAR => ['bla','bla']
);

my $arrayname = "FOO";
my @strings = @{$arrays{$arrayname}};
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What's the bigger picture? That is: what is it that you want to use this technique to achieve? What you have at present (apart from @${arrayname} should probably be @$arrayname)

It may be that you are trying to do something like:

my @FOO;

routine ();
print "@FOO";

sub routine
{
  my $arrayname = "FOO";
  my $string = "\@$arrayname = ('foo', 'bar');";
  
  eval $string;
}
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Prints:

foo bar
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If so, don't. Almost certinally there are better ways to do it, whatever it is.

The bigger picture is that I have config files that are perl code. Not my choice but I'm trying to make some tools work within that system.
I need to pluck strings from those config files, which *fortunately* do conform to the format given in my original post. Then I need to do stuff with that array of data (specifically lookup a bunch of hosts and delete any that don't resolve, but the purpose will vary with time I'm sure)
So, I can parse it out with regex if need be, but would prefer a quick win since it really is a valid hunk of perl.
I've tried PPI and my head hurts so I won't go there again :)

Are you trying to execute the content of the config files? If so, a simple require "config.pl" (or whatever the config file/script is named) will do that.

If you just need to extract specific information from the config file without executing it, then that gets a bit trickier, yeah. I can't really say how to handle that case without a sample of what one of these files looks like, which contents you want from it, and what you want to do with them.