If you want the hash name for debugging messages and that sort of thing, pass the name as an additional variable.

But what I want to talk about is the body of your subroutine. keys ${$hname} returns a list. Instead of going through the list item by item, in good C style, why not use idiomitic Perl: if you assign a list to a sscalar, the variable is assigned the number of elements in the list.

sub check_limit {
    my ( $href, $name ) = $_;
    $name ||= '<unnamed>';     # assign text if not provided

    my $num = keys %{$href};
    print "Hash: $hname has $num keys\n";
}
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