What is the proper name for a 'conspiracy wall'?

Solution 1:

In the film-drama context I've come across crazy board, or crazy wall.

Here's a definition from Esquire men's magazine:

Crazy Wall is the catch-all term for the boards on which investigators pin up and plot out all their clues in crime and spy thrillers, and recently it has become unthinkable for almost any serious TV drama not to have some sort of board for the characters to contemplate as they try to work out the kinks of a theory.

As @nnnnnn mentioned, there are other phrases -- investigation board or link board/chart -- used in real-life criminal investigations. Here for instance from the independent

Cops do still use link charts, but they're more helpful in complex, longitudinal investigations where there might be hundreds of people, places, phone numbers, IP addresses, etc. involved. There is now software for managing this kind of information.