The two crossword solutions for the term 'Big Name in Mattresses' are Serta and Sealy. Serta is an American company that has been manufacturing mattresses since 1931. It is one of the largest mattress companies in the world and is known for its innovative designs and technologies. Sealy is another American company that has been producing mattresses since 1881. It is one of the oldest mattress companies in the world and is renowned for its quality and comfort. Both Serta and Sealy are well-known names in the mattress industry and have become synonymous with quality and comfort.