Querying a SQL Server's CNAME alias instead of the actual instance name
The reason the CNAME is not working is you are using a named instance.  When you specify the name of the instance as in SERVER\INSTANCE the SQL Server client looks up the port number of the instance via the SQL Server Browser service.  Because you are using a name that is different from the actual SQL Server instance name, that lookup fails.  

Instead of connecting via AN-UATSQL03\DWH, try connecting directly using the port number, as in:

tcp:AN-UATSQL03,xxx


Where xxx is the port number.  You can get the port number either from SQL Server Configuration Manager, or via this query:

SELECT SPID = @@SPID
    , InstanceName = @@SERVERNAME
    , InstancePortNumber = CONVERT(varchar(255), local_tcp_port)
    , dec.auth_scheme
    , USER_NAME = USER_NAME()
    , SUSER_SNAME = SUSER_SNAME()
    , dec.connect_time
FROM sys.dm_exec_connections dec
WHERE dec.session_id = @@SPID;


You'll need to ensure the port number is not being assigned dynamically; use SQL Server Configuration Manager to set it to a manually configured TCP/IP port.  These Docs should help you out.

This query in your question implies you have a SQL Server linked server setup:

SELECT *
FROM [ALT-STG-SQL-ATLNTA1\DWH].[Database].[dbo].[Column]


If you only want to access the DWH instance via that linked server, you can simply define the linked server using the "real" name, but name the linked server object the aliased name.  Something like this should work:

EXEC master.dbo.sp_addlinkedserver @server = N'AN-UATSQL03\DWH'
    , @srvproduct=N''
    , @provider=N'SQLNCLI'
    , @provstr=N'SERVER=ALT-STG-SQL-ATLNTA1\DWH;'
    , @catalog=N'tempdb';


That would allow you to reference the linked server as [AN-UATSQL03\DWH] while actually connecting to [ALT-STG-SQL-ATLNTA1\DWH].  So your sample query would be:

SELECT *
FROM [AN-UATSQL03\DWH].[Database].[dbo].[Column]