The answer on this question relies upon the specific requirements of each insurance company, so there is no answer that will apply to each situation. We can help with some generalities, please add your experience in the comments to help future visitors.

Most companies do not charge for a person with a learner's permit or require the learner be named on a policy (but some do).

Once your daughter gets her permanent license, she must be covered under your auto insurance, unless she won't be driving. Newly licensed drivers are involved in more accidents than more experienced drivers, so their rates are considerably higher.

There is more information pertaining to teenage drivers in the auto insurance Learning Center at CarInsurance.com. You will need to notify your insurance company when a driver in your household gets a learner's permit.