I have to add that you only use "Здравствуй" to greet one person with whom you are on informal terms. In fact, this is most commonly used by adults greeting children.
- Здравствуйте, Наталья Александровна!
- Здравствуй, Ваня!
Children or friends usually use "привет" to greet each other, "здравствуй" is not wrong, but not common.
I never quite figured out if the diminutive form of the name equals an informal setting and therefor requires (or allows) the informal use of the greeting, or if it's okay to use the singular version - lacking 'те' at the end of 'здравствуйте' - when you are referring to a single person anyway.