Can a stored procedure reference the database in which it is stored?

I want to reference the database in which the stored procedure is stored, even if it is executed [from] another database.

Just use one-part or two-part names in the stored procedure, and it will reference objects in the database containing the stored procedure. In particular,

For static SQL in a stored procedure:

• Unqualified object names will resolve relative to the schema containing the stored procedure.

• Two-part names will resolve relative to the database containing the stored procedure.

For dynamic SQL in a stored procedure:

• Unqualified object names will resolve relative to the default schema of the user identity running the stored procedure (by default, the caller).

• Two-part names will resolve relative to the database containing the stored procedure.

The db_name() function will return the name of the database containing the stored procedure in both cases.

Here is a quick example that I put together showing common functions used to get close to what you are looking for.

/** Create a procedure in master to demonstrate
    DB_NAME()
    OBJECT_SCHEMA_NAME()
    OBJECT_NAME()
    @@PROCID
**/
USE [master]
GO

CREATE OR ALTER PROCEDURE dbo.uspTestMe
AS
BEGIN

    PRINT 'Database: ' + DB_NAME()
    PRINT 'Schema Name: ' + OBJECT_SCHEMA_NAME(@@PROCID)
    PRINT 'Procedure Name: ' + OBJECT_NAME(@@PROCID)

END

GO

/** CHANGE Context to TempDB
    Execute procedure in master
    **/
USE [tempdb]
GO

EXEC master.dbo.uspTestMe 

GO

/** Cleanup in master **/
USE [master]
GO

DROP PROCEDURE IF EXISTS dbo.uspTestMe