Until fairly recently it was impossible to change your domain with Google Apps for work (formally known as Google Apps for business). Its clunky but its now possible. This could be useful for a number of reasons such as you have an old domain you want to get rid of but had to keep because it was tied to the account.
You need to have super administrator privileges to do this. You will also need to have the domain that you want to be the primary domain already added as a secondary domain. In other words both domains have to exist in your Google Apps account under domains in the admin panel for this to work.
Firstly go to this link and press try it now
Press the Authorize requests using OAuth 2.0 so its on. Make sure the admin.directory.customer is ticked and press Authorize as the screen shot demonstrates below.
A box will appear asking to confirm. Press authorize. The screen then changes.
In customerKey field enter my_customer .
In fields field enter customerDomain .
Click Request body field, a drop down box will appear. Select customerDomain .
It the box that now appears enter the Secondary Domain which you want to change to the Primary Domain.
Below is an example:
Finally click the blue EXECUTE button.
When the process is done, your secondary domain is converted to the primary domain and the old primary domain becomes a secondary domain.
The final step is to cleanup the OAuth 2.0 permission you gave. Simply find the user in the Google Apps console who you used to make the change click Security and revoke the api access: