If I understand your problem correctly, this is how I'd do it (without all that mucking around with /s and /m and paragraphs)

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11123126
use warnings;

my %hash;
my $current;

while( <DATA> )
  {
  if( /(\w+):\n/ )
    {
    $hash{$1} = $current = {};
    }
  elsif( /(\w+):(\w+)/ )
    {
    $current->{$1} = $2;
    }
  }
use Data::Dump 'dd'; dd \%hash;

__DATA__
first:
this:that
here:there
when:what
how:where
now:later
name:onlyfirst

second:
this:that
here:there
when:what
how:where
now:later
name:onlysecond
[download]

Outputs:

{
  first  => {
              here => "there",
              how  => "where",
              name => "onlyfirst",
              now  => "later",
              this => "that",
              when => "what",
            },
  second => {
              here => "there",
              how  => "where",
              name => "onlysecond",
              now  => "later",
              this => "that",
              when => "what",
            },
}
[download]

Is that the hash-of-hashes you are looking for?