Is excluding my middle name on a graduate application acceptable?
Here is how I handle these things:


I publish papers with just my first and last name - no middle name or initial.
My vita and website use just my first and last name. 
When I fill out "official" forms, like employment paperwork and tax forms, I use the full name that is on my passport and driver's license.  This helps to avoid any confusion when these forms are compared with each other.  


For a school application, I would use the same name that is on your government ID. But this is just for the centralized records. Nobody in the academic department is likely to care (or even notice) if you just go by your first name and last name in public life.