Can you get car insurance on a car without the title in your name?

Not necessarily.

Auto insurance is of several types.

There is physical damage coverage, which pays for the repair of the vehicle if it is damaged. In order to obtain that, you must have an "insurable interest" in the vehicle. This means that you must have a stake in the continued existence (or good condition) of the car. Therefore a person who has loaned money for the purchase of the car with the car as collateral, has an insurable interest. That person may or may not be named on the title.

There also exists liability insurance. This compensates an injured person or entity for damages resulting from an automobile collision that was not his/her/its fault. It also protects the insured from a claim for negligence by hiring a lawyer to defend any resulting lawsuit, and paying damages for which the insured is found to be legally responsible. It is not necessary to own a car in order to get liability coverage. A person can purchase "non-owners coverage" that provides liability protection regardless of the vehicle being driven.