is it possible you can remove the invalid names before going through the list? for example create a new array with the valid names.. find the number of them and then test the id against the array element in your subroutine:

my @raw_names = ...;
my @valid_names = ();
my $total_valid_names = -1;

foreach my $raw_name(@raw_names){
     next unless $raw_name;
     push(@valid_names,$raw_name);
     $total_names++;
}
for(my $i=0;$i<length(@valid_names);$i++){
     check_name($valid_names[$i],$i);
}

sub check_names{
     my($name,$id) = @_;
     if($id == $total_valid_names){
        say "$name is the last name! ($idth)";
     }
}
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