If USER1 doest not specify databases in connection, we get connection error Cannot connect to xxxx.xxxx.database.windows.net. Login failed for user 'NT AUTHORITY\ANONYMOUS LOGON'. (Microsoft SQL Server, Error: 18456)

As per MSDN BOL documentation here

Reason:

Generally user does not have permission to connect to a database (i.e. Azure AD user has not been granted CONNET permission to a database he tries to connect to.

Solution:

Please check user connect permission

For further your ref Quickstart: Azure SQL Database: Use SQL Server Management Studio to connect and query data , How to create a linked server to an Azure SQL database and Azure SQL Database and SQL Data Warehouse access control

If USER1 doest not specify databases in connection, we get connection error Cannot connect to xxxx.xxxx.database.windows.net. Login failed for user 'NT AUTHORITY\ANONYMOUS LOGON'. (Microsoft SQL Server, Error: 18456)

As per MSDN BOL documentation here

Reason:

Generally the user does not have permission to connect to a database (i.e. Azure AD user has not been granted CONNECT permission to a database he tries to connect to.

Solution:

Please check user connect permission

For further your ref Quickstart: Azure SQL Database: Use SQL Server Management Studio to connect and query data , How to create a linked server to an Azure SQL database and Azure SQL Database and SQL Data Warehouse access control