Run the following commands in the master database. You will need admin rights on the server to execute them. oldname is the old name of your DB and newname is the new name.
sp_dboption 'oldname', 'single user', 'TRUE'
sp_renamedb 'oldname', 'newname'
-- The database name 'newname' has been set.
sp_dboption 'newname', 'single user', 'FALSE'
1) The .MDF and .LDF file names will not be renamed.
2) The Logical Names of the databases will not change. You can change these through MS SQL Studio Manager.