I recently read the book The Girl on the Train by Paula Hawkins. I found the way the story is told based on the different viewpoints of the main characters very interesting. Is there a name for this kind of style? Is it a common style?
It's called many things, but the most common terms seem to be multiperspectivity (what Wikipedia uses), alternate point of view, multiple narrative, and switching point of view. Multiperspectivity, however, seems to be a bit of a broader term - it refers to more than just literature.
It does seem to be a fairly common style (at least now) - I know Rick Riordan uses it in his books rather obviously (first person POV for different people in each chapter), but it also appears in, e.g., The Color Purple with the inclusion of letters from another character to the main character that are repeated verbatim in the text of the book. Wonder by R.J. Palaccio uses it, where there are four parts, and each part is narrated by a different character. (I'm thinking about this more and more, and a lot of new YA books seem to use multiple narrative, actually.) As I Lay Dying by Faulkner famously uses it.
The idea has actually been around for awhile, with some of the oldest novels in the english language epistolary novels - i.e., novels made up of letters between different characters showing their different viewpoints.