The term 'Big Name in Wine' can be summarized by two crossword solutions: Rossi (5 letters) and Gallo (5 letters). Rossi is an Italian winery founded in the 19th century by Giuseppe Rossi, and is now owned by the Marzotto family. It is known for its Amarone and Valpolicella wines. Gallo is a California-based winery founded by Ernest and Julio Gallo in 1933. It is the largest exporter of wine in the United States and produces a wide variety of wines, including Chardonnay, Cabernet Sauvignon, and Zinfandel. Both Rossi and Gallo are well-known names in the wine industry.