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while (my($name,$n1,$n2)=split(' ',<INFILE>) {
   # do something...
   }

open FILE, "< file2.txt" or die;
my @file2= <FILE>;  # read the whole thing
close (FILE);

foreach my $hit (grep /^$name\w+/, @file2) {
   my($name_2,$n1_2,$n2_2)=split(' ',$hit); # same as you did before.
   print "Found $hit\n" if $n1 == $n1_2;
   }