You might let people know what country your passport is, for reference or comparisons.

But I've never booked a ticket using my middle initial or name, even though my passport has my full name in it. I book lots of tickets for my Vietnamese friends, and I just book theirs as surname in the "last" part, and do either their first only or first and second, whatever they wish, in the "given" part.

I really don't think it will be important, but that's just my opinion.