MySQL user permission on stored procedure

I've created a simple stored procedure:

mysql> CREATE FUNCTION hello (s CHAR(20))
    -> RETURNS CHAR(50) DETERMINISTIC
    -> RETURN CONCAT('Hello, ',s,'!');
Query OK, 0 rows affected, 1 warning (0.00 sec)

But failed to run it:

mysql> SELECT hello('world');
ERROR 1370 (42000): execute command denied to user ''@'localhost' for routine 'test.hello'

Is it possible that my user name is an empty string? How do I create users and grant privileges? Can I grant a user all the privileges on all entities within a database?

As the error message itself says that user do not have the execute permissions.

mysql> SELECT hello('world');
ERROR 1370 (42000): execute command denied to user ''@'localhost' for routine 'test.hello'

You need to grant the Execute Permission to that user.For that you need to login as root user and grant the permission as

grant execute on db.* to user@localhost;

For your other queries :

-
Yes It is possible that your username is an empty string but it is not safe to create the users like this.

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For creating and granting privileges in brief have a look at This Link.

-
Yes you can grant all the privileges on all entities within a database.
for this you can execute a command like

Login as root user and issue a command

GRANT ALL ON DB_NAME.* TO 'USER'@'HOST' IDENTIFIED BY 'PASSWORD' WITH GRANT OPTION;

StackExchange Database Administrators Q#20221, answer score: 3