If you have already established a relationship with the coach, and you feel comfortable, it might be helpful to test the waters sharing what you feel comfortable about if he/she is asking. Would you want to run for a coach who responded negatively to something like that?
If you don't know the coach, you can probably make minimal true comments, like sharing the city you grew up in, etc.
If you feel uncomfortable, it's fair to say so, but just remember that I am sure no coach is intending to bring up a tough conversation in asking you these questions.
My best advice as a college coach and recruiter: If the coaching relationship is very important to you, be yourself as much as you feel comfortable. You will ultimately be yourself for the next 4-5 years and if you can see who you connect with upfront, you'll find the best fit, and so will the coaches recruiting you. If one specific school is your top choice regardless of the coach, the coach will be happy to hear this if he sees you as a fit for the team.
Good luck.