What about reading the file in chunks? "endmodule" seems like a good candidate for the separator.

#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

local $/ = 'endmodule';
my $name;
while (<>) {
    if (/^ \s* module \s+ (\S+?) \s* \( \s* .*? \s* \) \s* ;/xsm) {
        $name = $1;
        say $name;
    }
}
say "LAST MODULE (Perl $]): $name";
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