You cannot renew it under your own name without filing for a probate action. You can renew it under his name, but without filing a probate sooner or later, there is no way to transfer the title into your name.
When someone passes away, then their estate has to be distributed. The problem is that without probate - with assets such as titled property or bank accounts (those that do not have a pay on death clause) - this is hard to do. This is because you cannot switch over the assets without an order from the probate court, and simply a Certificate of Death will not do. A Certificate of Death simply states that someone has passed on, but does not give you the right to really do anything in the deceased's name.
So one files probate. Once probate is filed, the Executor of the estate gets something called a Letter of Testament/Administration (hereinafter "Letter"). This Letter will allow the Executor to switch over the assets from the deceased individual to whoever will own the property. It is like a "Power of Attorney," but from the Court. Without that Letter, there is no way to transfer titled property and switch the assets into the beneficiaries' names.
If there was a Will, the beneficiaries are decided per the Will. If there was no will, the beneficiaries are decided by default succession law of the state.
If he had a smaller estate, his estate may qualify for a quicker version of probate - see HERE and HERE.
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