Here is a little gem I found in the cisco forum that explains where to find and set the Default Domain and DNS Server(s) for Cisco ASA AnyConnect Users.
- Log into ASDM, select Remote Access VPN, expand Network (Client) Access, highlight Group Policies.
- On the right, edit the Group Policy assigned to your remote users.
- In the Group Policy edit screen that is displayed, highlight Servers on the left. This will show you the DNS Servers specified for the policy
- Click the small circle with double down arrows on the right to show more options. This will show you the Default Domain specified for the policy.
- Once you’ve edited the policy to meet your needs, click OK to save.
- Finally, save the running config to flash.
Test by reconnecting via an AnyConnect client and running an ipconfig /all.