No middle name isn't uncommon, perhaps one in five people. One middle name is most common.
A second middle name isn't at all unusual. Having three suggests an aristocrat — not common, but certainly understood.
I remember a Christian friend choosing his second middle name, which I thought was weird: https://en.wikipedia.org/wiki/Confirmation#Confirmation_name
http://www.onwhichsubject.com/piran/press/
We used to rely on this guy to break systems. Not using his name, mind; he's just a really devious programmer.
Now that I think about it, in a large chunk of the Slavic world (Russia, Ukraine, Belarus etc), the majority of people probably have no middle name. A patronymic isn't really a middle name as such.
We were still using punch cards back then.