The title of this book in the Hebrew Bible is "The Proverbs of Solomon, the Son of David, and King in Israel" (cf. 1:1). The Greek Septuagint called this book "Proverbs of Solomon." The Latin Vulgate named it "The Book of Proverbs." Translators of English Bibles place Proverbs among the poetic books (Psalms-Song of Solomon), whereas in the Hebrew Bible it is found among the "Writings," the third and final major section.
There is some debate about whether 1:1 is the title of the whole book or just the title of the first major section (chapters 1-9). The first view has in its favor the fact that the Hebrew Bible took the verse as the title of the book. According to this view the references to Solomon in 1:1 are an indication that he was the primary author of the proverbs in the book.  The second view is that 1:1 simply introduces the first major section of the book.
The support for this view is that some succeeding sections begin with a similar caption (cf. 10:1; 24:23; 25:1; 30:1; 31:1). However, chapters 1-9 do not contain "proverbs" as such, but longer wisdom speeches. In either case, the book got its title from the proverbs it contains. The whole book is a book of proverbs, so the title is appropriate.