When you want to rename the database then firstly check new database name should not exist.
Syntax:-
RENAME DATABASE oldDatabaseName TO newDatabaseName
Example:-
Suppose you have database employee_management and you want to change the name to employee_system and you want to use below command
RENAME DATABASE employee_management TO employee_system
Now, you can check the database name is changed through below command
SHOW DATABASES
Output:-
employee_system