I think this is more Perlish and neater:

use strict;
use warnings;
use LWP::Simple;
while (<DATA>)
{
   my ( $url, $name ) = split( '\s+', $_, 2 );
   # the 2 on the end stops it splitting on the space in "NY Times"
   chomp($name);
   print "Getting $name from URL $url\n";
   my $source = get($url)
     || die "Can't get website $name from $url: $!";
   open( LOG, ">$name.txt" )
     || die "Can't write to file $name.txt: $!\n";
   print LOG $source;
   close LOG;
}

__DATA__
http://www.yahoo.com/ Yahoo
http://www.cnn.com/ CNN
http://www.google.com/ Google
http://www.nytimes.com/ NY Times
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