Specifically, does the focal length change? How can this be rationalized?
It might help to think about the symmetry of a sliced biconvex lens.
If the biconvex lens can focus light from point F1 to F2, both distance $f$ from the lens, then when you cut the lens in half, each half will have a focal length equal to $f$.
The focal length of the biconvex lens is $f/2$.
The general lensmaker's equation, from Wikipedia, is
This entry about the Lens' maker equation in Wikipedia may help you:
Can calculate the ratio of focal lenghts before and after cutting by doing $R_2\rightarrow\infty$ and $d\rightarrow d/2$.
The focal power of the second surface that now is plane will be smaller (actually 0) and, unless this is compensated by a huge decrease in thickness, the lens will have longer focal distance. That's what intuitively seems to happens with the dimensions used in real-life lenses.