Using my own cookies

I automatically generate the specific cookie for visitors. Even after setting up the name of the cookie in config.php & tracker.php, I'm not able to store the value of my cookie in user's browser and It uses default Tracker cookie model.
How can I store my own cookie value?

Start by reading config.php and tracker.php to trace how the configured cookie name and value are handled. Reproduce the reported behavior and determine why the default Tracker cookie is used instead of the visitor's cookie. Done means the configured cookie value is stored in the user's browser and the default model is no longer used.

Written by the indexing model from the issue text.