In FileMaker, you define a value list with StudentID# in field 1 and the student name in field 2. Since you are limited to just these two fields, it may require a calculation field or (better) a text field with an auto-entered calculation that combines names from first and last name fields in order to get a full name into the Field 2 spot in the value list. This value list will display the student name, but enter the ID into the field.
If you set a validation rule (that's why an auto-entered calc is better here) on the name field to insure unique names, you can hide the first field from view when the value list is deployed by selecting the "Show values only from second field" option. (To get a unique data in the second field, it is sometimes helpful to include more data in the second field than just a name such as an address or phone number.) If you format the field as a pop up menu, the field will display the student name in this field when you exit the field even though the ID number is what is actually stored in the field. You can also use a drop down list, but then you need a relationship to the table of student names and numbers so that you can add a field to your layout from this related table to display the student name. This name field can be placed next to or even on top of the Drop down list formatted ID field.
With scripted support, it's also possible to set up a drop down list that auto-completes on the student name and which includes code to handle cases where the name selected matches more than one student.
Here's a demo file that includes that approach: http://www.4shared.com/file/plr_jbkk/EnhancedValueSelection.html