My dad wants to put my name on all his bank accounts as a safety precaution if he dies?

In order to protect your benefits and stop them from thinking that any money in your fathers accounts belongs to you then when he adds your name to his accounts your father also needs to grant you Power Of Attorney.

Power of Attorney is a legal document that allows your father to appoint you as his legal agent to protect him and his estate and it gives you the authority to make medical decisions, Financial decisions, health care decisions, monitor bank accounts, sign contracts for him ect and other things on his behalf.

Power of Attorney is a much better safety precaution than just adding you to his accounts.
Power of attorney also shows that the money in his accounts doesnt belong to you and that you are only safeguarding it on his behalf.

Dad needs to put his accounts in the name of a living trust with you as trustee.

He doesn't have to put you on the accounts. He can make arrangements with the bank to have the accounts paid out to you in the event of death. That way you don't have full access and shouldn't interfere with any benefits.

You need to get in touch with a lawyer or estate planner.
What your dad is thinking is right, however, if your name is on the accounts then you can be held responsible for the debts.

There may be other ways to handle this .

you are benefit scum or whatever