The if($write_new) block is only activated if there are names in file2 that don't appear in file1
Hence the following works:-

open FIRST,"file1" or die "Can't open file1: $!\n";
open LAST,"file2" or die "Can't open file2: $!\n";

my (%names1,%names2) ;
my $write_new = 0 ;

while (<FIRST>)
{
   /(\w*) (\d*)/ ;
   $names1{$1} = $2 ;
}
close FIRST;

while (<LAST>)
{
   /(\w*) (\d*)/ ;
   $names2{$1} = $2 ;
}
close LAST;

   open NEW,">","file3" or die "Can't open file3: $!\n";
   foreach (sort keys %names2)
   {
      if (defined($names1{$_}))
      {
         print NEW "$_ $names1{$_}\n" ;
      }
      else
      {
         print NEW "$_ $names2{$_}\n" ;
      }
   close NEW ;
   }
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It means that file3 is always opened, but I can live with that.
Thanks for your help