Yes, because when you die, all your debts will be her responsibility to pay off.
She will need to know all information about your policy and where you keep your policy so that she can access it when it's needed. And you need to know about hers as well.
Have the guy who is selling it to you go to the DMV and get a new title.
Do this BEFORE you buy it - otherwise, it could be stolen and then you're in trouble.