You should also be checking your opens and using strict.

#! perl -w 
use strict;

open(MYOUTFILE, ">$ENV{HOME}/tmp/design_name_dnp_top") 
  or die "Could not open design_name_dnp_top for writing: $!"; 
open (FILEH, "$ENV{HOME}/tmp/strfile") 
  or die "Could not open strfile: $!"; 
while (<FILEH>) {
  chomp; 
  /\/([^\/]+)\d$/; 
  print MYOUTFILE $1."topdnp\n"; 
} 
close(FILEH); 
close(MYOUTFILE);
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