As far as I know (and honestly, I really can't be bothered to check something like this), Granit Xhaka has always worn the number 34. In fact, I'm pretty sure he literally has a tattoo of the number 34. When he was first rumored to be coming to Arsenal months and months ago he made a joke about asking Francis Coquelin to drop the number if he came. We all pretty much assumed that Granit Xhaka would wear 34 at Arsenal.
Granit Xhaka will not be wearing 34 at Arsenal.
Since Aaron Ramsey dropped 16 in favor of Mikel Arteta's old number 8 shirt, the 16 was in fact open, so it's a fair choice. I'm curious about why it's not 34, though. Did Xhaka decide against asking a new teammate to drop a number for him, considering Xhaka's probably taking Coquelin's place in the squad? Does he just have respect for the Arteta-Ramsey midfield, and so he wants to repeat the 8-16 combo?
Either way, the smaller the number the better. Good choice, Granit.