For this to work, the service account for SQL Server needs to have access to the share. Many times, you have a local machine account as the service account, for instance NT Service\MSSQLSERVER. Access to external resources will then be through the machine account. So things may work better with a real account. But even then the NAS must understand Windows accounts.
Given that you don't have a domain, it would be difficult of the NAS would be a Windows fileserver. You would need to run SQL Server under a Windows user, and the fileserver would need to have a user with the same name and password.