Because the public wants to know that the situation is under control. Given the disorganized response to the first shooting, the public is rightfully skeptical of certain skillsets of the local law enforcement community. Additionally, the conflicting "persons of interest" sends the message that there still may be someone out there, unlikely as that is, but people want and need to be reassured.
I think telling the public that the guy is dead should be pretty reassuring as to the fact that the matter is under control. I don’t think knowing his name would add much to that, and might harm the investigation.