Use split on each line of input. So, it will look something like this:

while (my($name,$n1,$n2)=split(' ',<INFILE>) {
   # do something...
   }
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Note that split with a pattern of a single space, as shown above, has a special meaning. Read about split in perlfunc.

Prep your file2 by reading the whole thing into an array.

open FILE, "< file2.txt" or die;
my @file2= <FILE>;  # read the whole thing
close (FILE);
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Now, use the grep function to check for matches against the array. Inside the "do something..." body of the loop above,

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;
   }
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That's untested, but should give you some ideas. This introduces some "Perl ways" without being too thick to understand for a novice.

Good luck.

—John