Question

When is it unnecessary to follow a direct quotation with a parenthetical citation that includes the name of the source

Answer 1

Parenthetical citations are not needed when the direct quotation is common knowledge.

Things that fall into the category of common knowledge are proverbs or well-known quotations. "To be or not to be" would not be cited because it is part of common knowledge. "A rising tide lifts all ships" is a proverb that would not be cited. Parenthetical citations are used to identify the source of the quotation. They typically include the author's last name and page number (if available). If the author's name is unknown, the title of the work is used. When the author and/or title of the work has been stated in the introduction to the quote, then only a page number would be needed. 

Answer 2

Parenthetical citations are not needed when the direct quotation is common knowledge.