Can I have a scalar function and a stored procedure with the same name?

We use a stored procedure to generate an internal number (accessible via the OUTPUT keyword).

As you cannot use the stored procedure inside a statement, I thought it would be a good idea to just create a function which just calls the stored procedure with its parameters and returns the OUTPUT value. So I could directly use it for statements.

Is it possible to name a stored procedure and a scalar function the same in one database, and is this a good idea?

To simply answer the question (thanks to Martin):
No, I can't.

The error message raised is Error 2714 ("There is already an object named 'Foo' in the database.").

A complete name of any relational object in a database is a name in two parts :

1. the schema name, that is in fact a container inside the database
2. the object_name, that is an unique name relative to the schema

As a demo you can do :

CREATE SCHEMA S_SQL;
GO
CREATE USER U_SQL WITHOUT LOGIN WITH DEFAULT_SCHEMA = S_SQL;
GO
GRANT CONTROL TO U_SQL;
GO
EXECUTE AS USER = 'U_SQL';
GO
CREATE FUNCTION F_FOO()
RETURNS CHAR(3)
AS
BEGIN 
   RETURN 'foo';
END;
GO
REVERT;
GO
CREATE PROCEDURE F_FOO
AS
RETURN 'oof';
GO
SELECT ROUTINE_NAME, ROUTINE_TYPE 
FROM INFORMATION_SCHEMA.ROUTINES;

You will have the same object name, but in two differerent schemas...