Partnership rules

Hi, my wife and I operate a side business as a partnership (not ltd.), in the same way one would operate a sole proprietorship. We need to buy a vehicle for our business & wonder how to do this. All accounts and utilities are done with our own names as we operate out of our house. Is it ok to buy the car under one of our names and just claim it under the business or do we need to buy it and register it under the business name? (Not sure how we could even provide proof of address for the business - literally the only thing we have with the business name is the actual business registration document). Please advise if it's ok to just use my name and then claim it as a business expense. Thanks in advance!