Names in The Namesake

The Namesake had me as well thinking about names, particularly how somewhere in the transition between cultures something as simple as a name becomes complicated and frustrating.
The scene when Gogol is starting Kindergarten as Nikhil felt all too familiar. Mrs. Lapidus's insistence on understanding why he had two different names despite her brains obvious inability to wrap itself around the idea of names in a non U.S context is something that I've experienced many times. She frowns before saying,

"I'm not sure I follow you, Mr. Ganguli. Do you mean that Nikhil is a middle name? Or a nickname? Many of the children go by nicknames here. On this form there is a space..."

Abimbola is not my middle name despite the fact that it's sandwiched between names # 1 and #3 on my birth certificate. As well, Patricia is not my first name, even though it's name #1. And yet I have always had to explain my name in the context of first, middle and last name.What is it about schools that makes this structure so important?