Yes. You can do PG or Doctorate from the same University.
To practice medicine in India, MBBS should be from a recognised University.
PG qualification will be registered in India as an additional qualification over and above MBBS. Benefit of additional qualification in India is Practice as specialist and for academic job and Govt. related departments.
However, if the purpose of doing PG is to register as an additional qualification and for specialist medical practice in India, then PG from UK, USA, AUSTRALIA, CANADA & NEWZEALAND only are recognised.
Otherwise, if the purpose is other than those specified above, PG can be done from any University .