Punctuation of Initials in Name

Answer

1. Wikipedia and the NYT write the author's name as J. K. Rowling and J. K. Rowling

2. The author herself chooses this form, © J.K. Rowling and © J.K. ROWLING (note the use of block capitals)

3. The Guardian, a British newspaper, favours this form: JK Rowling, author of 15 books…

If you're looking at omitting the dot/period, I would personally avoid adding spaces between the initials, e.g. J K Rowling. But people are free to write their name as they please.

References
A Wikipedia page of authors whose first and middle names are abbreviated; e.g. D. H. Lawrence, J. D. Salinger, T. S. Eliot, J. R. R. Tolkien, etc. They all follow the same format.

In their manual of style/abbreviations, Wikipedia says [emphasis mine]

Use initials in a personal name only if the name is commonly written that way. See Wikipedia: Manual of Style/Biographies for when to use full names and other formats.

An initial is followed by a full point (period) and a space (e.g. J. R. R. Tolkien), unless:

• The person had or has a different, consistently preferred style for his or her own name. In that case: treat as a self-published name change; examples include k.d. lang and Jeb Bush.
• An overwhelming majority of reliable sources do otherwise for that person; examples include CC Sabathia.

It seems that the British convention is to omit the dot (period) in names that have initials. The Independent has an article about people whose middle initials are invented. Famous examples include; Ulysses S Grant, Harry S Truman, Michael J Fox, and JK Rowling.