I just want to ask. my parrents are deceased. do i need to write their names on the form. What sort of checks does the home office do? Do they contact my home country to check. Also if a sibling is havin problems withe home office will this affect my application for naturalisation?

The form states that this info is used to see if you have automatic rights to British Ntionality. I don't know why you think it is a problem? You shold be able to provide that information when asked by home office

IMO, it does more then that because it also identifies you with your parents. My name is very common in India and Pakistan and they need to identify me as an individual. There will be a 1 in a million chance that another person will have my name and his father name same and probably not a chance to have my name, my father name and my mother name as same.  So they also need to make sure that they are identifying you as an individual.

I don't think anyone will be able to provide you proper answer here and your best bet is to check with home office. If I am in your shoes I will just put parents name in the space provided unless  you are hesitant about it.  If so, then Home Office may refuse your application and wonder why you have not put their name and what you have to hide. Remember, this is not a right and according to home office it is just a priviledge.