A writer underlines the name of a newspaper when he is composing a hand-written document, according to Purdue University's Online Writing Lab. When a writer is composing on a word processor, using italics for a newspaper name is recommended.
Underlining a word and using italics have the same basic purpose. They allow certain words to stand out from the rest of the surrounding text. Italics and underling are generally used for creative works such as plays, books, movies, magazines, poems, works of art and newspapers.
As a rule, the word "the" is not italicized or underlined even when it is part of the title.