Can I rename a module?
Renaming a Drupal feature requires additional steps than rename a custom module.

Solution 1 (without un/install)


Backup the DB.
Put the site on maintenance mode.
Rename the feature with an IDE or bash script (don't access/edit any content of the site while you are doing this).
Run: 


drush php-eval 'registry_rebuild();' 
drush updb -n. (forces drupal to reload caches related to module/features)
drush cc all



Solution 2 (more proved but requires un/install)


Backup the DB.
Follow the steps to rename the feature on this thread.


To replace the new name (the human and the machine name) on each file, I suggest you to use an IDE like NetBeans (or similar).

You can also use cool unix commands like sed and find to do it.

Try to make a code review after the changes to make sure that the rename was done on the right places.

Note: to make sure that the name I choose for a module/feature is not already used, I use the following command:

drush pm-list --type=Module --no-core --status=enabled --pipe | sort