I'm a PGY-1, so allow me to take this one.
Many specialties require a intern year of something before starting specialty training in earnest. ENT, for instance, requires a year of general surgery for its intern year. For radiology, one can do a year of internal medicine, a preliminary year, or a transtional year (there are specific 1 year programs designated as preliminary or transitional - they are usually quite similar). Some residency programs for these specialties have integrated the intern year, so those in training stay at one institution for the duration. Most do not, however, so people end up choosing to do their intern years at places different from where they will undertake the bulk of their training.
Example: one of my classmates matched in neurology. His program integrated the required internal medicine intern year, so he will stay at one institution and do 1 year of IM followed by 3 years of neurology.
Another classmate matched in radiology at our alma mater. For personal reasons he is doing a transitional year (a pretty cushy one, from what I hear) at a private hospital outside of town. Then he will do 4 years of radiology. Situations like this may explain why you have seen different hospital names on peoples' CVs.
To get back to you, internal medicine does not require anything beforehand, so you will start as an IM intern and finish in 3 years total. That's the lingo.