Hello

I will give you all the steps but I personally insist thet you should inform your school about it (where you have studied in both 10th and 12th) and let them suggest you a course of action.

Step 1- You have to get the Application Form (you can do it from the respectve board's website or your school).

Step 2- Filling of the form

Step 3- Documents submission ( SLC, xerox of a page of admission and withdrawal register wrt you)

Step 4- Fee ( since you have to change your father's name the cost will be Rs 1000+ the cost of the original document)

Step 5- Submit the documents along with the application to The Principal of your school and  to your board.