Name vs Passport for purchasing JR Pass

Hi. I want to purchase a Japan Rail Pass. I will be traveling to Japan in October.
To purchase the JRPass, I need to enter my name on the JRPass website. It asks for my first and last name, and says that the names must match the names on my passport. My US passport has my first, middle, and last name. If I only enter my first and last name on the JRPass website (that is, no middle name), will that cause a problem?
Thanks
Brian