Try
SELECT @caller = OBJECT_NAME(@@PROCID)
EDIT:
After you got current proc. name, pass it to log sp as parameter, that's it.
This only works inside of stored procedure.
An example on using this
USE AdventureWorks;
GO
IF OBJECT_ID ( 'usp_FindName', 'P' ) IS NOT NULL
DROP PROCEDURE usp_FindName;
GO
CREATE PROCEDURE usp_FindName
@lastname varchar(40) = '%',
@firstname varchar(20) = '%'
AS
DECLARE @Count int;
DECLARE @ProcName nvarchar(128);
SELECT LastName, FirstName, Phone, EmailAddress
FROM Person.Contact
WHERE FirstName LIKE @firstname AND LastName LIKE @lastname;
SET @Count = @@ROWCOUNT;
SET @ProcName = OBJECT_NAME(@@PROCID);
RAISERROR ('Stored procedure %s returned %d rows.', 16,10, @ProcName, @Count);
GO
EXECUTE dbo.usp_FindName 'P%', 'A%';
More on this
http://msdn.microsoft.com/en-us/library/ms174408(SQL.90).aspx
An example on stored procedure logging. Can be useful
http://weblogs.sqlteam.com/brettk/archive/2006/09/21/12391.aspx
Here's a related question also
http://stackoverflow.com/questions/713677/can-a-ms-sql-stored-procedure-look-up-its-own-name
EDIT 2: and other related question in SO
http://stackoverflow.com/questions/148004/find-out-the-calling-stored-procedure-in-sql-server