I don't really understand what you are getting at here!

I don't really care what you consider is the difference between a middle name and a given name. As far as most people are concerned, if your name is Bessie Annie Smith, then Annie is the middle name, because it comes between Bessie and Smith. It's the name in the middle, so it is a middle name.

As an aside, I think that all your names are "given" - being given to you by your parents. Are you talking about the name you are usually known by?

My husband has four names, First-name, Second-name, Third-name and Surname. All his life, he has been known as Second-name, but with the introduction of computers and travel requirements, he has to use First-name for all his travel bookings, ESTA etc.

Based on our experience with my names, husband's names, and getting ESTAs, I still think that the OP is over thinking and obsessing about something that will not cause him a problem.

And I still maintain that it is the US criteria he has to satisfy and comply with, not his own country's interpretation of naming practices. And the US will say that any name that comes in between two other names is a middle name.