What are functions with the property $f(f(x)) = x$ called? Do functions which, when composed with themselves, are equivalent to the identity function (i.e. functions for which $f(f(x)) = x$ in general) have a name and if so, what is it?
Additionally, am I correct in saying that a such function has a splinter of two, or is it perhaps splinter of size 2 or something else entirely? Or could I say that a such function has an orbit of size 2? 

These are involutions. The orbits of an involution all have size $1$ or $2$.
What is a splinter?
