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`;