Yes, the DMV requires auto liability insurance to register a vehicle in New York .
Okey, I have a bit of a problem: I have a different name on both my vehicle registration application and my Insurance Identification Card, do they have to be the same or that woudn't be a problem?
Yes, that's a problem. Your insurance cards and vehicles must have the same name.
I'll sort that out then. I want to know what sort of proof will I receive after getting the insurance?
Your insurance company will issue a proof of insurance in two ways: 1) They will either give you to original NY state Insurance Cards or provide you with acces to your digital electronic NY State Insurance.2) They will send  an electronic notice of insurance coverage  to the DMV.
excellent explanations now I have a question can I pay by mail?
Follow the instructions in your suspension order. Send the bottom of the order along with a certified check, personal check, or money order made payable to the Motor Vehicle Commissioner for the fine
and how much should i pay if my insurance term is 90 days?
If your insurance term is 90 days, you can pay a total fine of $ 900 $ 8 per day for the first 30 days = $ 240; plus $ 10 per day for 31 days at 60 = $ 300; plus $ 12 per day on days 61 - 90 = $ 360 and not delivering your dishes; or you must turn in your plates and complete a 90 day registration suspension
Could you tell me what is the main theme?