When I purchased this cactus from a private individual who was selling her cactus collection before moving out of state, she told me she wasn't sure the plant tags were accurate because many of the cacti had fallen over and when she was straightening them, she just stuck the loose tags in the closest pot. The plant tag on this cactus was labeled Gymnocalycium multiflorum, which is the old name for Gymnocalycium monvillei. I have my doubts about the species, although it's definitely a Gymnocalycium.
After it is older, the body form and spines will be more characteristic of whatever species it may be. Once it flowers, the shape, size and color of the flowers will give another indication of the species. If it is a G. monvillei, it will have large white to light pink flowers. It takes 5-6 years from seed before this species flowers. Judging from the size of this cactus it's obvious that it is a few years away from flowering
Although the G. monvillei is a clumping species, the way this cactus is doing it is out of the ordinary. This specimen is growing heads all over the body, rather than near the base. If this type of clumping is not some rare malformation, then it could be an indication that it has been misidentified. I guess only time (or a cactus identity expert) will tell.