Hello,
I've just recently had to address the same issue in my environment and also had difficulty in finding documentation. I did find this: Supporting Always On Availability Groups (SQL Server) with App Volumes - VMware Blogs which provided some useful information. The steps I completed were:
1. I stopped the "App Volumes Manager" service on the App Volumes Manager server
2. Our DBA migrated the App Volumes Database
3. On the App Volumes Database server I opened "ODBC Data Source Administrator (32-bit)"
a. On the "System DNS" tab I selected "svmanager" for the 32-bit platform and clicked "configure"
b. In the next screen I updated the server name
c. We are using SQL server authentication, so I provided the Login ID and Password on the following screen
d. From there I kept all of the remaining defaults.
e. After clicking finish I tested the connection to verify
4. I restarted the "App Volumes Manager" service
