If the administrator creates your database for you when setting up your permissions, you can begin using it. Otherwise, you need to create it yourself:
mysql> CREATE DATABASE menagerie;
Under Unix, database names are case sensitive (unlike SQL keywords), so you must always refer to your database as menagerie, not as Menagerie, MENAGERIE, or some other variant. This is also true for table names. (Under Windows, this restriction does not apply, although you must refer to databases and tables using the same lettercase throughout a given query. However, for a variety of reasons, the recommended best practice is always to use the same lettercase that was used when the database was created.)
Creating a database does not select it for use; you must do that explicitly. To make menagerie the current database, use this statement:
mysql> USE menagerie
Database changed
Your database needs to be created only once, but you must select it for use each time you begin a mysql session. You can do this by issuing a USE statement as shown in the example. Alternatively, you can select the database on the command line when you invoke mysql. Just specify its name after any connection parameters that you might need to provide. For example:
shell> mysql -h host -u user -p menagerie
Enter password: ********