You may be able to change your license without changing your insurance or registration but it would not be advisable. To be truthful to the state of New York and insurance company you should inform them of the change of address.

If you did not inform your insurance provider of your new principle address where you garage the vehicle and were in an accident, this omission of information may be seen as misrepresentation on your side and cause your claim to not be paid.

Most state's Departments of Insurance will tell you that the single most important thing you can do to protect yourself from a claim denial is to, make certain that all of the information you provide your insurance company is complete and accurate. 

According to the New York DMV, to change your address on DMV documents you write the new address on your documents. Write your new address in the available space on the back of your driver license, learner permit or non-driver photo ID card.

On your NYS registration document, carefully draw lines through the old address and write your new address. Do not change the address on your title certificate. If you write any change on your title certificate, the certificate is not valid. Your title certificate is valid with your old address.

To change the address on your driver license and your vehicle registration at the same time, you must use form MV-232 or call the DMV Call Center. If you provide a new address when you renew or replace your driver license, that transaction does not change the address on your vehicle registration or your title certificate. If you provide a new address when you renew or replace your vehicle registration or your title certificate, that transaction does not change the address on your driver license.