The first problem that I had with your code was the confusing name, $namecnt. I expected a numeric scalar for that type of name!
I changed that var name to "$names2count" to imply multiple names which will be counted - I assume in a case insensitive manner.
Added: William test case

use strict;
use warnings;

my %name_count;

my $names2cnt='David|Tom|Sam|Will|Dave|William|Thomas';

while (my $line = <DATA>)
{   
   next unless ($line =~ /\S/); #skip blank lines
   my $name = (split (":",$line))[2];
   
   $name_count{$1}++ if $names2cnt =~ /\b($name)\b/i;
}

foreach my $name (sort keys %name_count)
{
   print "$name => $name_count{$name}\n";
}

=prints:
Dave => 1
Will => 3  #allows Will and WILL and WiLL spellings
William => 1
=cut

__DATA__
1:NAME:Bob:Bobville:Phone

2:NAME:Dave:Davis:Phone
3:NAME:Will:Willard:Phone
4:NAME:Todd:Toadlane:Phone
5:NAME:WILL:Street:Phone
6:NAME:WiLL:Street2:phone2
7:NAME:WilliaM:xyz:1234
[download]

Update: I'm not sure that this \b stuff in the regex is necessary. I put some obvious test cases into the code, but not all possible test cases.