Something like this works fine for me as well.
Code:
SELECT man.name, count( emp.employeeid ) AS num_employees
FROM employee man, employee emp
WHERE man.employeeid = emp.managerid
GROUP BY man.name
If you add emp.name into your select statement, you will not get the proper results because you are grouping by manager. (You'll only get one employee name...)
Also as a side note, if you store a manager as managing themself, your count may not be returning exactly what you want...