[dba-SQLServer] Renaming the database / files

I want to rename a database, both at the file level and at the name level
(what SQL Server sees it as).  I am afraid to just rename the files
themselves lest there be some something somewhere that causes it to fail to
reattach.

How is this done "the right way"?

John W. Colby
Colby Consulting
www.ColbyConsulting.com