A relatively easy way to do this is to brand each CAS server's OWA logon page with the server name. This way, end-users are able to provide the server name if they run into problems.
For Exchange 2007, navigate to C:\Program Files\Microsoft\Exchange Server\ClientAccess\owa\auth folder and open the logon.aspx file using Notepad.
Add either of the two edits shown in the screenshot below:
Adding the server name as highlighted above in red will visibly add the server name to the logon screen, as shown below:
Adding the server name as highlighted above in blue will add the server name "invisibly" below the logon screen. To view the server name, click anywhere on the screen and press CTRL-A to select all. You can then see the server name, as shown below:
For Exchange 2010, navigate to the C:\Program Files\Microsoft\Exchange Server\V14\ClientAccess\Owa\auth folder and open the logon.aspx file using Notepad.
Add the server name, as shown in the screenshot below:
This will add the server name to the logon screen, as shown below:
Important Note: These edits are overwritten anytime an Exchange Server update is applied to the CAS servers. This is because every update includes a complete reinstallation of the Exchange binaries, and the logon.aspx file you edited will be overwritten.
Typically, the logon.aspx page rarely changes, so you can usually make a copy of it after you've made your edits and copy it back after the update. However, there are no guarantees that the file will not be changed by an update. If so, you will need to re-edit the logon.aspx file.