always wanted to be

I'm almost certain that "had always wanted" is the most proper, and that "always wanted" is acceptable colloquially.

We would use the first if we were telling a story about, say, Rowling's struggles to become an author. We're beginning from the days before she published and using that as our frame of reference.

The second would be used if we start our story from Rowling as an established author, and then flash back to her pre-author days. The past perfect is generally used when you go backwards in time, in relation to where you are in your story.

I think the third is acceptable if we start our story with the present day. The present perfect is used to combine the past and the present in many interesting ways. Since Rowling wanted to be an author in the past AND she probably wants to continue her career at present, the present perfect can work. I probably wouldn't use it, though, mainly for the reason you outlined - she is an author now, and would like to remain so for the foreseeable future. There are better ways to express that idea with less confusion.

Really, the choice you make depends on where on the timeline of Rowling's career you're starting the story.

"J.K .Rowling always wanted to be an author." is referring to her in the past tense while using the word "always" - which suggests to the reader that she may no longer be with us in this world...

If this were written about me, I might be offended. Of course, context is key. Probably passable, because we all know that she is in fact an author now, so can assume you are simply neglecting to add "before she became one" etc., and if I knew that you were referring to a period of time during which you knew J.K .Rowling personally, then it would also fly.

I would say that the "had always wanted to be..." form would only be proper if she no longer wants to be an author -- perhaps because she no longer enjoys it, or, of course, if the person no longer lives.

Ing: your examples actually point to the idea that the sentence immediately preceding the one in question has more to do with it than the timeline. When you say 'He is happy' since 'is' is present tense, then in the following sentence you use 'has wanted' which is also the present tense of a past (and supposedly current as well) notion. If you change your second example to be: He got the letter yesterday. He was happy. He had always wanted. then I don't think you could use 'has always wanted' in that case.
I'll still agree that the first sentence has a lot to do with what you say in the second (you likely wouldn't say he got a letter in 1980 and he is happy immediately afterwards). But I think that timeline has less to do with it than the voice that's being used.
What I learned in school is tense agreement. You can't simply change from past to present whenever you feel like it.

"J. K Rowling always wanted to be an author." ~ (Simple Past) A simple statement about her want before current time. We could also read into it and think she is now an author.

"J. K Rowling had always wanted to be an author." ~ (Past Perfect) Meaning she wanted to be an author but now doesn't want to be one.

The simple past is used for things that happened in the past. The past perfect is usually used with a reference point. It isn't often used to refer things into the past. History books are written with the simple past not the past perfect.

"J. K Rowling has always wanted to be an author." ~ (Present Perfect) Meaning she has always wanted and still wants to be an author.

As she most obviously is an author the present perfect version ('has always wanted') doesn't make an awful lot of sense, unless it was taken from some interview with her before her first book was published. Like the questioner, I think 'be' here really means 'become', as in 'She wants to be a doctor when she grows up'. Although I usually find myself in agreement with porsche, I don't go along with the 'continue being' argument.

And I agree that the past simple version sounds as though she's either no longer with us, or that it never happened - 'She always wanted to be an author, but circumstances didn't allow it.' Considering she is one, and very much alive, it sounds a bit strange to me.

Past perfect (had always wanted) is usually used together with past simple to show a 'past before the past', so it would definitely make sense in a context like 'she had always wanted to be an author, so she enrolled on a creative writing course'. But if you accept the argument that 'be' in this context is more like 'become', then that 'be' has already been accomplished in the past, so the past perfect version would in fact be the most appropriate, because her wanting is in the past. Once you've got something you don't need to want it any longer.