A CRM Organization’s unique name is the name of the organization as it referred to internally. For example, it’s the name of the SQL database.
Usually, the organization unique name is simply the Friendly Name with any illegal characters ( spaces, punctuation, etc. ) removed from the name.
For sample: CRM Accelerators is my friendly name, but crmaccelerators is my unique name.
There was a change introduced into CRM Online with Update Rollup 3 that made the unique name the Organization’s Globally Unique Identifier ( GUID ) with the dashes removed.
While I doubt that this will affect to many people, it is a little disconcerting to see the unique name in that formation.
You can find the organization unique name under Settings, Customizations, Developer Resources you will see something like this:
Note: This is from an On-Premise organization.
Note: This is from an Online organization.