That's probably not a good idea. That said, eval might be the answer.

sub xyz {
   my ($tgs) = @_;
   return eval <<"END_OF_SUB_XYZ";
   my %Test_hash_$tgs;
   my \$other = "Why did I do this?";
   print "\$other  Now I have to escape so many things.\n";
END_OF_SUB_XYZ
   ;
}
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But again, let me emphasize, I do not recommend that.

Then again, maybe a symbolic reference would work, but that's disallowed by use strict.

sub xyz {
    my ($tgs) = @_;
    my $hash_name = "Test_Hash_$tgs";
    my %{$hash_name};
}
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My guess is that it would be best to have a hash of hashes.

sub xyz {
    my ($tgs) = @_;
    my %Test_hash{$tgs} = {};
    # use $Test_hash{$tgs}{foo}, etc.
}
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It might help to have a look at perlref.