If you work with records as units rather than with lines things get a little easier:

use warnings;
use strict;

my @records;

local $/ = "\n\n";
while (<DATA>) {
    my ($title, $row) = /TEST\s+\w+\W+(\w+)\D+(\d+)/;

    next unless defined $row;
    push @records, [$title, $row];
}

print "$_->[0] -> $_->[1]\n" for @records;

__DATA__
data per sample
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Prints:

CUSTOMERPHONE -> 1300
CUSTOMERORDER -> 0
CUSTOMERCARE -> 530
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Note that @records is used to preserve the order of the data in the source. The reversion to using a hash should be simple and obvious.

Your script looks very elegant as compared to mine. I didn't think of using $/ as a delimiter between each 'records'.

Building on that base, I suggest...

Unless you are absolutely sure that the input will always be in exactly the right form (now and in the future), it's a good idea to do something when the regex doesn't match -- at least a diagnostic message indicating that something isn't as expected. Along the lines of:

  if (my ($title, $row) = /TEST\s+\w+\W+(\w+)\D+(\d+)/) {
    push @records, [$title, $row];
  }
  else {
    warn "no match at $." ;
  } ;
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Of course you could make the warning message more helpful, or do something else to flag the problem.

In passing, when I checked this fragment I noted that the regex is "widely drafted" (as the lawyers would say). For real (as opposed to example) code it's a good idea to tighten up the regex, so that it doesn't happily provide duff results from duff data.

1. next if /^\s+$/ skips lines containing nothing but whitespace, but doesn't skip lines that are completely empty. Use next if /^\s*$/ or next unless /\S/ instead.
2. The capturing regexes used to extract title and row aren't anchored. Use m/^\s(\D+)$/i and m/^\s+(\d+)$/i.
3. In the final map, you iterate over %record. Iterate over keys %record instead.

You have two problems. First, when you capture title you're attempting to capture non-digits (e.g. /(\D+)/). The trouble is that whitespace also qualifies as non-digits. So you're creating empty titles from time to time, which explains the funny whitespace when printing out the blank keys. Try instead to capture only what you're looking for, i.e. characters that aren't digits, or /([A-Za-z]+)/.

Second you're printing out the hash, but really you want to map over the keys of the hash. Add the keyword keys in front of the hash to get the desired result, otherwise the map iterates over key, value, key, value, etc..

Ugly but quite short code:

while (<>) {
    next unless /CUSTOMER/;
    my $count = (<>, <>);               # WTF
    s/^\s+//, s/\s+$// for $_, $count;
    print "$_ -> $count\n";
}
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