Troubleshooting Resource Governor / Classification Function
Make sure your group name returned matches (identically) to your actual workload group name. Some times, I've found, it's helpful to reconfigure even if it doesn't say it needs to be done.

use master
GO

-- Create a test DB which our CF will be based on
CREATE DATABASE RGDB;
GO

-- enable RG
ALTER RESOURCE GOVERNOR RECONFIGURE
GO

CREATE FUNCTION dbo.RGClassifier()
RETURNS sysname
WITH SCHEMABINDING
AS
BEGIN
    IF (ORIGINAL_DB_NAME() = 'RGDB')
        RETURN N'OriginalDBWG'

    RETURN N'Default'
END
GO

-- Create a new Pool
CREATE RESOURCE POOL OriginalDBPool
WITH (
MAX_CPU_PERCENT = 10
)
GO

--Create a new WG
CREATE WORKLOAD GROUP OriginalDBWG USING OriginalDBPool
GO

ALTER RESOURCE GOVERNOR WITH ( CLASSIFIER_FUNCTION = dbo.RGClassifier)
GO

ALTER RESOURCE GOVERNOR RECONFIGURE
GO


Open a new query window after running this and check the pool name by running:

SELECT wg.name FROM sys.dm_exec_sessions s inner join sys.dm_resource_governor_workload_groups wg on s.group_id = wg.group_id where s.session_id = @@SPID


Then, change the connection and add in an additional parameter

database=RGDB;


Then run the query again. You should see the workload group name change.