At the moment the manager name field matches the full name field of the manager.
That could be a problem if a manager ever changes their name (such as due to a change in Marital Status). I recommend that you use an ID number that identifies the manager instead of their name. A drop down list or pop up menu for selecting an employee's manager can list the manager names but enter the selected manager's ID.
Whether or not you make that change, what you describe is called a conditional value list. I have amassed a fairly extensive links on the subject. For what you describe, you probably need only read the first or second link and then, if you need to see more, download the demo file. But I'll include the other links for future reference.
There's a lot of overlap between the first two links so you can read one and skim the other. The demo file gives you several examples of different conditional value lists so you can examine them to see how they are set up. If you are using FileMaker 12 or later, you can open this demo file from your File menu to get a converted copy of the demo file that you can examine in your version of FileMaker.
The next to last link discusses how to set up a chain of conditional value lists where the value selected in each conditional value list controls the values listed in the next value list and the very last link is a fairly new addition that describes how to use ExecuteSQL to produce conditional value lists that aren't easily possible with the other methods described here.
Forum Tutorial: Custom Value List?
Knowledgebase article: http://help.filemaker.com/app/answers/detail/a_id/5833/kw/conditional%20value%20list
Hierarchical Conditional Value lists: Conditional Value List Question
Using ExecuteSQL to produce a conditional value list: Using ExecuteSQL to Produce a Conditional Value List
Feel free to post follow up questions here if those links aren't enough to get your value lists working correctly.