You can rename an organisation but only for CRM on premise.
The reason for this is because you need to temporarily disable the organisation, rename it and then enable it again.
To do this you need to go to the Deployment manager
Select the Organisation you want to rename
Click the disable button on the right menu
When you click on the disabled organisation you now have the option to edit the organisation. This will now allow you to change the display name of the organisation
After you have changed the display name it will run through changes this link on the report server and SQL databases.
Now you need to enable the organisation
Now next time you login you will see the new name of the organisation under you user name on the top right of the CRM 2011.
One thing to point out is the url for the organisation will remain the same. If you want to change that then you will need to uninstall and reinstall. You can delete organisations after you have disabled them in the deployment manager.
As always make sure you back up everything you rename or delete organisations or any other major changes to your CRM environment