Try changing the job owner to sa, or something with very high level permissions. Usually the job will take the owner of who created it.

If the service account you use is not a domain admin, the anonymous login error is usually related to the service account used for sql not being able to register the spn and also not having delegation setup.

The anonymous logon message ("Login failed for user 'NT AUTHORITY\ANONYMOUS LOGON") was resolved by making two changes to the AD environment.

•Allowed the service account to "write public information” to self.

•Allowed Kerberos delegation to any on the service account then stopped the SQL Service and started it again.

Used setspn -L MSSQLSvc/myhost.redmond.microsoft.com:1433 accountname to check for registration. -- example only

After this was successful I checked SQL authentication between servers using

SELECT auth_scheme FROM sys.dm_exec_connections WHERE session_id = @@spid to make sure it said Kerberos.