I want to buy some stock photos like the ones below. What is this design called?
I don't even know how to start searching...
'Flat vector illustration' is a very nice blanket term and should be a good start for your search query to find more of these. You might consider adding 'material design', Google's version of 'flat design'.
Though note that 'material design' is primarily a UI/interaction set of guidelines more than just an illustration style.