What is the name for the wall behind the suspect in a mug shot?

It doesn’t really have a particular name. It’s just a wall with height markings in feet on it. However, sometimes people do refer to it as a “police lineup wall”. That because it’s the kind of thing they use in police lineups.

Notice the handcuffs in your image? It’s making some sort of comment related to getting arrested or being in jail, or having one’s mugshot taken. For example, from The Usual Suspects:

You see this sort of wall markings all the time now in convenience stores and other places liable to be robbed. That’s because that way the video conveniently takes a picture of the bandits with their height clearly documented.

That said, the standard police lineup technique doesn’t work very well, and some jurisdictions have switched to sounder methods. But the markings left on pillars next to checkout counters for video cameras to snap pictures of still have their own uses.

I have seen "mug-shot wall," "mugshot wall," and also "Rogue's Gallery" for something with a little flavor that describes the whole scene--wall and lineup. Rogue's Gallery could also refer to a collection of individual mug shot photos, so the usage would have to reflect that you are describing the criminal lineup.