do i have to give rest home my fathers savings if my name is on the accountm
Yes, his share or portion of the money (i.e. that part contributed by him, whether from other savings or assets, his wages/salary, social security or pension, etc.) is *his* share of the money, and the rest home or Medicaid is entitled to it. You are only entitled to that share of the money which you can prove you contributed or which came from you. Putting your name on the account does not itself protect his money or assets from being spent for his care.