If you are looking to use Data Driven Pages.
As far as I know, ESRI doesn't provide a tool to do this.
The Calculate Adjacent Fields tool requires somthing like 8 additional fields in your index grid.
To avoid having to add additional fields to your index grid at all, I suggest a different approach.
You can use the Boundary Labeling with Maplex to achieve a decent result. I have a few other tricks I've figured out to provide an even better result.
I have attached a Microsoft Word Document that explains how to set up your labels once you have your atlas created.
Post back here if you have any questions.