Mr. Rajesh
I feel very sorry and sad that ur father is no more.
Coming to your problem of changing name of your father in your marks card: i am of the following opinion-
1) There is no need for you to change your fathers name that to after his demise as even according to you your fathers name is stated as "Thimmegowda urooof puttaiah" wherein I feel that "uroof" means Alias as as such therecannot be any objection to any body with regard to your fathers name,
2) According to you it is only in your marks sheets that your fathers name is printed as only Puttaiah, which I think cannot be any hindrance for u to get your fathers assets transferred in your name if you can get for yourself a Legal Heir Certificate to the effect that u r the child of so called "Thimmegowda uroof Puttaiah".
3) Even otherwise if u wish to change ur fathers name in your marks card you can approach the concerned Board in Education Department and ask for change of your fathers name showing all necessary documentary proof with regard to your fathers name, your name and that you are legal heir of your father.
4) The other way is you can approach a court of law for seeking declaration to the effect that names "Thimmagowda Puttaiah and Puttaiah" are the names of the one person only, of whom you are the legal heir.