Making a new database onto existing AWS RDS instance
CREATE DATABASE db2;


There does not have to be a different user for each database.  But you might want to do it if you want to keep, say, two applications, each using one of the databases, from accidentally stepping on each other.

GRANT ALL PRIVILEGES ON db1.* TO 'user1'@'host-name' IDENTIFIED BY 'password1';
GRANT ALL PRIVILEGES ON db2.* TO 'user2'@'host-name' IDENTIFIED BY 'password2';


Usually I have a separate user for each database; sometimes I have a user that touches multiple databases.

(This answer applies to MySQL and MariaDB in general.)