Here are my suggested settings for the cookie information for phpbb:
Cookie domain:
set this to either:
www.******
or
.******
Notice the two periods in the second one
Cookie name:
Any name will do, for example, "phpbb" or "forums" but it is suggested that if you run two forums on the same domain that you give each of them a unique name.
Cookie path:
The path to where your forums reside. For example if your forum is located at *****/phpbb/ then you would enter /phpbb/
If your forums reside at *****/forums then you should enter in /forums/
Here is an example of how I have my cookie settings for my site poetrypages at http://www.poetrypages.com/phpBB2/
Cookie domain: www.poetrypages.com
Cookie name: poetryforums
Cookie path: /phpBB2/
Using the same formula as suggested above I have never had a problem with my cookie settings on any of the many phpbb forums I run.
Also, if you change your cookie settings and want to test out the new settings you may want to clear out the old stored cookies for your forums before reloading the page and trying it with the new settings.