The author or authors' name or names are never italicized. Adhering to the rules of capitalization, authors' names are written in the normal way. There are several academic writing styles--and one, Associated Press (AP), specialized for journalism--and though they differ on some points of writing style, they consistently agree that authors' names are not italicized. The one exception to this is when an author's name forms part of a book or play title, such as in this made-up example, After Jane Austen Wrote and Came to Dinner.

The various writing style guides used for academic writing are put out by these organizations: Modern Language Association (MLA), used in literature and other language-centered academic writing; Associated Psychology Association (APA), used for academic writing in social sciences; University of Chicago, Chicago Manual of Style (CMS), used by various academic institutions and by some journalistic institutions; Turabian, based upon CMS but simplified for unpublished academic works; Harvard University, Harvard Author-Date style, used widely for general academic writing.

None of these style guides allow for putting author names in italics. For the short story "Boys and Girls," your reference in MLA style would specify Alice Munro, "Boys and Girls," Dance of the Happy Shades.

There are several styles used in writing academic papers. "Style" in this context means a complete set of standards for things such as citation format, title page, font, spacing, abbreviations, and punctuation. Which style you should use depends on your academic discipline, country, and the instructor's preferences. In the United States and Canada, the most common academic styles are MLA (Modern Languages Association), Chicago (University of Chicago Press), and APA (American Psychological Association), while journalists tend to follow AP (Associated Press) style. In Britain and Europe, MHRA (Modern Humanities Research Association) style is common for academic papers. 

Alice Munro's “Boys and Girls” is actually a short story in a book entitled Dance of the Happy Shades. In most styles, neither the author's name nor the name of a short story is italicized, but the title of the book containing the story is italicized. You should also note that in British English, you should use single quotation marks and place punctuation outside the quotation marks, whereas in U.S. English one uses double quotation marks and places punctuation inside the closing quotation mark. 

No, you never italicize the name of the author, and you only italicize the title of the work if it is a book. If you are referring to a short story you put the title of the story in quotes. This is what you should do if your essay is about Alice Munro's story "Boys and Girls." (Notice that the period at the end of the sentence comes inside the closing quotation mark.) Titles of poems and essays and other short pieces are also put in quotes. Titles of plays are customarily italicized. You can see in the reference link below how Alice Munro's "Boys and Girls" is set off in quotes.