No, I've never heard anything to indicate that the Doctor (VOY) has any connection to the Doctor (Doctor Who).
The characters couldn't be more different - Doc (VOY) is placid and very tied to one location (sickbay, then Voyager). The Doctor is manic and travels constantly.
The EMH was called 'Doctor' because that's what he was - he had an advanced knowledge of every realm of medicine, and his life was dedicated to treating others and saving lives (and, eventually, self-improvement).
The Doctor...runs a lot. And people around him die (despite his best efforts in most cases).
In short, The Doctor chose his name for reasons only he knows. The EMH is called 'Doctor' as an acknowledgement of his skills, position, and because it simply fits. The EMH was not designed to have an individual personality, so he initially needed no name. Once Voyager was stranded, 'Doctor' sufficed as a unique identifier.