transfer of property

you can apply for name change in society along with formal letter and death certificate to Co-opeative society.

if probate required to do so than apply for probate as well.

If u r only legal heir of your father and your father MAKE a WILL in your name so u can give application in Society and attach a copy of WILL AND one Affedevit for legal heir then Society see the document and pass a resulation for that and enter your name  in Society records.