|If this employee is merely dropping names, and not dropping productivity, then this may be an issue in name only. Of all the problems that an employee can cause on the job, this has to be somewhere near the bottom of the list.|
In fact, a more serious problem at work occurs when a group of employees laughs at one particular individual. This is the key issue to address here. Your name-dropping employee may well have some underlying insecurities, but the fact that other employees are laughing at her points to more serious problems in terms of teamwork, respect, and support in your department.
This situation is best approached on two fronts. If you truly believe that name-dropping is a real problem, you need to do more than broach it with this employee. As her manager, you can have candid discussion and indicate that her tendency to do this may be creating some difficulties in her working relationship with the rest of the staff.
Speaking of the rest of the staff, this is probably a good time to consider implementing some team-building sessions and activities for the entire department. Perhaps if the department is operating as more of a team, an employee who is being excluded will not feel the need to drop names in order to be included.