My dad has dementia and does not drive anymore, his license expired. Do I have to put my name as owner of his car in order to drive it?

All very good answers here. The good two-step plan is to go ahead and cancel your father's car insurance and pay for storage.
However, selling the vehicle should be your best option overall. I can see how the POA does not give you this authority. You can put the insurance in your name without transferring the title, thus if it is still drivable, you can drive it.

Read your PoA doc. Does it give you authority to buy and sell things in his best interests? If so, this would include his car.

Also, if he's very elderly he's probably paying a high premium for insurance. If you're legally able, sell it and cancel his insurance. Then reimburse yourself for miles drive from his assets but keep a very detailed log, gas receipts, etc. There are apps that can do this.

FYI you should be in possession of the original copy of the PoA doc, not the attorney. YOU need to know what it says and understand what it empowers you to do.

Wait - I dont understand why the attorney said you cant sell assets while he is alive if you are POA . this does not make sense at all. Many people DO sell asset such as cars and houses as they need to free up the money to pay for his care. I would ask the attorney again.

What you cannot do is sell the car and pocket the money yourself .
What I believe you can do is sell the car, and add the money to savings which is used towards your dad's care .

You have a lot of power as POA and if you dont think your dad is ever going to drive again and need this car, then per my understanding, you could decide to sell it to free up the money for your dad's care.
As to whether you can drive it right now - why do you need to?

my dads car is garaged now. I stopped paying his insurance. Soon the registration will run out. Then soon I plan to sell it off.

You cannot put your name as owner of your father vehicle if you do not have title to the vehicle. What you can do is call your father’s car insurance carrier and tell them that you have POA for him and that he has dementia and he does not drive any longer and you would like your name listed on his car insurance policy as a permissive user or additional driver. You will have to send them a copy of the POA if your father cannot give the insurance company permission to add you to his car insurance policy.

You are POA. You can check on his insurance, and you SHOULD as you are responsible for paying it. You can be certain you are covered, and should before driving the car. Your POA also tells you if you can sell this car for your father if he needs funds for his care.

You should likely look into garage rental or storage for this car if it doesn't get driven.