An university, like any other corporate entity, generally has both the inclination and legal authority to regulate the use of its name, particularly when somebody is implying that something is officially endorsed by that entity.
There is another usage, however, that is harder to regulate, which is when a name is used in a descriptive manner. For example, the MIT Scheme implementation of the Scheme programming language was not originally named MIT Scheme: it was just Scheme, and when other implementations were created, the community started using the prefix "MIT" to distinguish it, and that ended up getting imported into the official name. When something like this happens, it's hard (and generally pointless) to fight common usage.
So should something like the "Berkeley Entity Resolution System" be understood to be claiming the name "Berkeley," or should it be better understood as a short way of saying "the Entity Resolution System developed by Berkeley"? Lawyers might well tussle over this, depending on the particulars of a case, but academics in many cases simply seem to proceed assuming the second and often find no objection from their institutions.