It can be extremely hard to tell parents about being transgender. If you aren't really sure how they'll react, you can start by talking to them about transgender people and watch their reactions. Also, you can write a letter, or email them, explaining yourself/to come out. It can be much easier to do than in person.

Heather is a good name, but it's ultimately up to you to make that decision. You can also change your mind if you find a name that to like better.