I looked at the current source of B::Deparse, and so far I've found two functions that are responsible for looking up variables. Hooking into these is a hackish way to get the variable names :-) There may be more things that need to be hooked (Update: and the final example shows it's not perfect), but perhaps this is a starting point:

use warnings;
use strict;
use B::Deparse;
use Data::Dump;
use Hook::LexWrap;

my $deparse = B::Deparse->new();
$deparse->ambient_pragmas(strict=>'all', warnings=>'all');

wrap 'B::Deparse::stash_variable', post => sub {
        my $rv = pop @_;
        my ($self, $prefix, $name, $cx) = @_;
        dd 'stash_variable', $prefix, $name, $rv;
    };
wrap 'B::Deparse::stash_variable_name', post => sub {
        my $rv = pop @_;
        my ($self, $prefix, $gv) = @_;
        dd 'stash_variable_name', $prefix, $rv;
    };

our $foo = "World";
my $bar = "Hello";
our @foo = 1..3;
my @bar = 4..5;
our %foo = ( abc => 444 );
my %bar = ( def => 222 );
our $ref = { xyz => 123 };
$deparse->coderef2text(sub {
        print "$bar, $foo\n";
        print "@foo @bar\n";
        print "$foo[1] $bar[1]\n";
        my %dummy = %foo = %bar;
        print "$foo{abc} $bar{def}\n";
        print $ref->{xyz};
    });

__END__

("stash_variable", "\$", "foo", ["\$foo"])
("stash_variable", "\@", "foo", ["\@foo"])
("stash_variable_name", "\@", ["foo", 0])
("stash_variable", "%", "foo", "%foo")
("stash_variable_name", "%", ["foo", 0])
("stash_variable_name", "%", ["main::ref", 0])
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I showed an example of PadWalker here.