Is it legal to buy a car under someones name if you have power of attorney and they are aware of the situation?

There must be a reason why you want to purchase a car under another person's name. You must have a bad credit history, must be a poor credit risk or there must be some other reason. What you are suggesting is fraudulent. A person who needs an attorney-in-fact to help with managing their affairs has not been fully informed if they have agreed to take full responsibility for a car loan for a poor credit risk. You would be abusing your authority if you carry out that scheme. If you check the statutory powers granted under a POA in your state you will not find that an attorney-in-fact can borrow money for their own personal use under the name of the principal. You should be replaced.