The term 'Big Name in Pineapples' can be broken down into several crossword solutions, including DOLE (4 letters), GRENADES (8 letters), PINAS (5 letters), ANANAS (6 letters), GRENADIER (9 letters), and CORER (5 letters). All of these solutions are related to the PINEAPPLE industry, with the most well-known being DOLE and DELMONTE. DOLE is a major producer of canned PINEAPPLE products, while DELMONTE is a major producer of fresh PINEAPPLE products. GRENADES and GRENADIER refer to the shape of the PINEAPPLE, which is similar to a grenade. PINAS and ANANAS are alternate spellings of the word 'PINEAPPLE, ' while CORER refers to the process of removing the core from a PINEAPPLE.