Bhagyanagar is not an 'old' name. It is just an alternate name. All the names used for Hyderabad originate from its founder, Quli Qutub Shah.
VSKP's name was not changed. Waltair and VSKP were twin towns. As time progressed, both towns grew and Waltair became a part of Visakhapatnam. Today, Waltair is a suburb of VSKP.
There were two stations in VSKP until 1964. The present day VSKP station was called Waltair Jn (WAT), and a short distance from WAT, there was another station named 'Visakhapatnam Town (VZT)'. In 1964, the VZT station was closed as the city had grown and the most of the inhabitants moved to the north, towards the Waltair area.
A few years later, the Waltair station was renamed as Visakhapatnam as Waltair had now become a suburb of VSKP and VSKP was the main city.