G'day lightoverhead,

As has already been pointed out, using symbolic references this way is a bad idea. If you're interested purely for academic reasons, see "perlref: Symbolic references"; understanding the refs stricture of the strict pragma would also be useful.

As an alternative, consider the technique in this script (and see the Notes at the end):

#!/usr/bin/env perl

use strict;
use warnings;

use Inline::Files;

my %master_hash;
my @filehandles = (\*FILE1, \*FILE2, \*FILE3);

for (0 .. $#filehandles) {
    my $fh = $filehandles[$_];
    my $wow_key = "wow$_";

    while (<$fh>) {
        chomp;
        push @{$master_hash{$wow_key}{(split /\t/)[1]}}, 'sth'; 
    }
}

use Data::Dump;
dd \%master_hash;

__FILE1__
x   file1line1
x   file1line2
__FILE2__
x   file2line1
x   file2line2
__FILE3__
x   file3line1
x   file3line2
[download]

Output:

{
  wow0 => { file1line1 => ["sth"], file1line2 => ["sth"] },
  wow1 => { file2line1 => ["sth"], file2line2 => ["sth"] },
  wow2 => { file3line1 => ["sth"], file3line2 => ["sth"] },
}
[download]

Notes

• I've kept much the same logic as you show in your OP.
• The wowN names you wanted are created and the hashes they refer to are easily accessible via a $master_hash{wowN} variable.
• I've had to guess at input data as you didn't show any. For demo purposes, I've used Inline::Files; for your real code, continue to use an array of filenames and open.