I also like to change the (internal) logical names of the database - otherwise they keep the name of the original
ALTER DATABASE MyDatabaseName
MODIFY FILE (NAME = 'OrigDatabase_Data', NEWNAME = 'MyDatabaseName_data')
GO
ALTER DATABASE MyDatabaseName
MODIFY FILE (NAME = 'OrigDatabase_Log', NEWNAME = 'MyDatabaseName_log')
GO
(but you will have to find out what the original names were)