Science Photo Library says that this photograph of Claude Shannon was taken in Bell Laboratories in 1954. What is the name of the computer behind him?
It's likely part of the Bell Model VI relay computer, installed at Bell Labs in 1949. This was a revision of the massive Model V designed and built by Bell, which were installed at NACA (1946) and BRL (1947).
The test panel next to Shannon is very similar to this Model V control panel (missing its fascia). This is not much of a help to identification, however, as Bell reused standard telephone racks, cabinets, switches and relays as much as possible.
The glimpse of the other panel through the glass door, showing "Control …", "Digits …" and "Register" above a large relay rack is more distinctive. The device may not have been a computer as we know it: the Model VI was not a stored program device, though it did have some features that came very close.