It is possible for someone to take away your car keys even if the car is under their name and you use it to get to and from work. This is because the legal owner of the car has the right to control who uses it and under what circumstances. However, if you have an agreement with the legal owner that allows you to use the car for specific purposes, such as commuting to work, then they may be violating that agreement by taking away your keys.
In terms of insurance, if the car is registered and insured under different names, it can make filing an insurance claim more difficult. However, if you are an adult and the car is in your name, you will need to purchase your own auto insurance policy. If someone else is listed on the title of the car, they may need to be listed on the insurance policy as well in order to be covered in the event of an accident. If you are a young driver and still living with your parents, staying on their car insurance policy can help keep costs low, but you must meet certain requirements.