It says here that:
This statement was added in MySQL 5.1.7 but was found to be dangerous
and was removed in MySQL 5.1.23. It was intended to enable upgrading
pre-5.1 databases to use the encoding implemented in 5.1 for mapping
database names to database directory names (see Section 9.2.3,
“Mapping of Identifiers to File Names”). However, use of this
statement could result in loss of database contents, which is why it
was removed. Do not use RENAME DATABASE in earlier versions in which
it is present.
You can import all data into a new database then delete the old one.
It is also possible to use the RENAME TABLE
statement using same from/to table name but different from/to database. There are a few catches.
CREATE DATABASE `test_bkp`;
RENAME TABLE
`test`.`table1` TO `test_bkp`.`table1`,
`test`.`table2` TO `test_bkp`.`table2`,
`test`.`table3` TO `test_bkp`.`table3`;