my() creates a variable in the current lexical scope. Since the "my $file" is in the while loop's condition, $file is created in the while loop and then goes away. Try this:

my $file;
while($file = readdir(DIR)) {
...
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Also, unless you have a bunch of other code in the while loop that needs to run, you should exit the loop once $bool becomes true (BTW--$bool is a really lousy name for a variable). Additionally, it is usually good practice in a regex match to use '^' and '$' to indicate line beginnings/ends, and '\A' and '\z' to indicate string beginnings/ends. This is not a strict requirement, and you'll usually be OK if you switch them around.

my $file;
while ($file = readdir(DIR))
{
   if($file =~ /\Amyname\.doc\z/i)
   {
         $bool = 1;
         last;
   }
}
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