Are the Hyderabad Central University and University of Hyderabad same? Whenever I search for HCU on the web browser I find multiple links related to UOH aside from HCU?

Yes, both Hyderabad Central University and University of Hyderabad are the same. It is called Hyderabad Central University nowadays, abbreviated as HCU. It was previously known as University of Hyderabad, UoH. 

Similarly, another example is of Delhi University which is called and abbreviated as DU, whereas it is officially called as University of Delhi.