Sharing session value between two different asp.net solutions using "SQL Server" mode

USE ASPState
GO

ALTER PROCEDURE dbo.TempGetAppID
    @appName tAppName,
    @appId int OUTPUT
AS

    -- start change

    -- Use the application name specified in the connection for the appname if specified
    -- This allows us to share session between sites just by making sure they have the
    -- the same application name in the connection string.
    DECLARE @connStrAppName nvarchar(50)
    SET @connStrAppName = APP_NAME()

    -- .NET SQLClient Data Provider is the default application name for .NET apps
    IF (@connStrAppName <> '.NET SQLClient Data Provider')
        SET @appName = @connStrAppName

    -- end change

SET @appName = LOWER(@appName)
SET @appId = NULL

SELECT @appId = AppId
FROM [ASPState].dbo.ASPStateTempApplications
WHERE AppName = @appName

IF @appId IS NULL BEGIN
BEGIN TRAN 

SELECT @appId = AppId
FROM [ASPState].dbo.ASPStateTempApplications WITH (TABLOCKX)
WHERE AppName = @appName

IF @appId IS NULL
BEGIN
EXEC GetHashCode @appName, @appId OUTPUT

INSERT [ASPState].dbo.ASPStateTempApplications
VALUES
(@appId, @appName)

IF @@ERROR = 2627 
BEGIN
DECLARE @dupApp tAppName

SELECT @dupApp = RTRIM(AppName)
FROM [ASPState].dbo.ASPStateTempApplications 
WHERE AppId = @appId

RAISERROR('SQL session state fatal error: hash-code collision between applications ''%s'' and ''%s''. Please rename the 1st application to resolve the problem.', 
18, 1, @appName, @dupApp)
END
END

COMMIT
END

RETURN 0 
GO

<sessionState mode="SQLServer" sqlConnectionString="Data Source=.;Integrated Security=True;Application Name=TEST" cookieless="false" timeout="20"></sessionState>
   <httpRuntime targetFramework="4.5"/>