From moly (informal term for molybdenum) + cow. The word cow alludes to the fact that the device “milks” technetium-99m from molybdenum-99: see quotations.
When the 99Tcm isotope is needed for medical imaging purposes, it has to be created on the spot because its half-life is only six hours. This is done using a device filled with longer-lived 99Mo, which decays into 99Tcm, continually replenishing the supply within the device. Because the process of removing the accumulated 99Tcm is called "milking", the device is informally known as a "moly cow."
2013, Paul Parsons, Gail Dixon, The Periodic Table: A Field Guide to the Elements, London:Quercus, →ISBN:
The radioactive isotope molybdenum-99 (half-life of 66 hours) decays to generate technetium-99m, which has a half-life of only six hours and is used in hospitals for medical imaging. The technetium isotope collects in various parts of the body, in particular bone. Scanners detect the radiation from the isotope to create an image, enabling diagnosis. The process uses a device that is filled with Mo-99, which decays into Tc-99m, forming a continuous supply that is ‘milked off’. The device is nicknamed the ‘moly cow’.
2013 November 6, Chary Rangacharyulu, “Radioactivity”, in Physics of Nuclear Radiations: Concepts, Techniques and Applications, Boca Raton, Fla.:CRC Press, →ISBN, page 43:
Clearly, transporting the daughter in equilibrium with the parent is a more economical, safer, and environmentally friendlier approach. This is the reason that "technetium generators," dubbed "moly cows," are transported around the globe instead of the 99mTc isotope.