The two crossword solutions for the term 'Big Name in Athletic Footwear' are Avia (4 letters) and Asics (5 letters). Avia is an American footwear company founded in 1979 that specializes in athletic shoes. Asics is a Japanese company founded in 1949 that produces a wide range of sports equipment and apparel, including athletic shoes. Both companies have become well-known for their quality products and have become popular choices for athletes and casual wearers alike.