MySQL: Cloning a MySQL database on the same MySql instance

 As the manual says in Copying Databases you can pipe the dump directly into the mysql client:

  mysqldump db_name | mysql new_db_name  

If you’re using MyISAM you could copy the files, but I wouldn’t recommend it. It’s a bit dodgy.

Integrated from various good other answers

Both mysqldump and mysql commands accept options for setting connection details (and much more), like:

 mysqldump -u <user name> --password=<pwd> <original db> | mysql -u <user name> -p <new db> 

Example : mysqldump -u root -pmypassword old_database | mysql -u root -pmypassowrd new_database