Here's a quick macro I wrote that sets the value of the Text1 field for any given task to the value in the Name field for the preceding task (ignoring the first task that has no preceding task). Very simple, but you can see how this sort of thing is possible. You can then just assign the macro to a button and click it anytime you want to update...
Code:
Sub setFieldText()
Dim temp As Long
For temp = 2 To ActiveProject.Tasks.Count
ActiveProject.Tasks(temp).Text1 = ActiveProject.Tasks(temp - 1).Name
Next temp
End Sub