Ryan P, I'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this!
Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I'll repost your solution in case you'd like to "Accept " the answer. Accepted answers show up at the top, resulting in improved discoverability for others.
Issue: Customer configured an Azure Storage account with file shares for use with hybrid identities, utilizing identity-based access with Microsoft Entra Kerberos. Default share-level permissions are enabled.
Mapping drives works initially on both Azure AVD VMs (multi-session Windows 11 Enterprise 22H2) and local hybrid-joined Windows clients (various Windows 10 and 11).
After a reboot, AVD clients encounter the "System error 1396" with the message "The target account name is incorrect." Physical clients and non-Azure VMs do not exhibit the same issue.
Error Message:
System error 1396 has occurred.
The target account name is incorrect.
Solution: Customer changed from using MS Entra Kerberos based access to AD DS based identity. Now everything works. Customer to setup Entra Domain Services and start moving devices/users, etc to the Entra cloud completely.