This is a bit long for a comment.
I would opt to remove the database name, but I don't know if this is a "best practice". When doing development, I sometimes have a tendency to keep multiple versions of the same database on a server. Specific database references in code would cause a problem. (A better development environment is to have another dedicated instance of SQL Server.)
However, you should think about:
- Whether your application uses only one database or multiple databases. If there are multiple databases, you might want to move stored procedures from one to another, so the explicit references would be useful.
- Any impact with your version control software.
- Your process for maintaining the database code, adding in new functionality and fixing problems.