In many states if you are starting with an out of state title, the motor vehicle folks will want to see the car and verify the Vehicle Identification Number before issuing a new title. Therefore, you can title and register your car as a Datsun if you do the title transfer before you begin the conversion process. If you drag or drive your car down there with a different body on it, you will likely get a Specially Constructed Vehicle (that's what they call them in Arizona, your jurisdiction may be different) title.
An SCV title can actually be helpful. For example, if you get pulled over by the constabulary you will not have to explain why your Italian sports car is registered as a Datsun! Usually SCV titles reflect both the donor car and what it's supposed to resemble, e.g., 1962 F****ri GTO/Datsun 280Z. However, it is possible to have them list only the first part. Just be careful about false advertising when you sell the car!
Insurance companies are more concerned about the running gear of the car and what it will cost to fix (if you want collision coverage as opposed to just liability). Therefore, insuring as a Datsun (provided you have not done an engine swap) will give them an accurate idea of the performance capability of the car, which in turn tells them how much of a risk it is to other peoples' property!
For collision coverage (i.e., fix YOUR car if you damage it), the insurance company wants to know what it's worth and what it will cost to fix. Insuring it as a Datsun is a sure fire way to have the insurance company total it with anything more than about $1000 worth of coverage. Many companies will do a "stated value" policy. This requires either documentation of build cost, or appraisal of value, or both. Your premiums will be proportional to this value.