What kind of variable is $name? If it's a lexical (my) variable, it won't be visible in the included file. You could make it a local, or you could eval the contents of the file:
open FH, 'included.pl';
my $text;
{
local $/ = undef;
$text = <FH>;
}
close FH;
my $name = 'turd';
eval $text;
die "error in included file: $@" if $@;