Sending a product on the Apple Store as a gift to a friend?
You have multiple questions here.

First see Apples instructions here http://store.apple.com/us/help/gifting

Will your Bank show and what, you can answer that based on prior experience. My Visa shows the Store name and the amount, not to whom is it shipped or what it was.

In your case better option might be a Gift Card, that you can mail your self, thus no trace.