The term 'BIG NAME IN RELIEF' can be solved by two crossword solutions: ADVIL (5 letters) and GasX (4 letters). ADVIL is a brand of ibuprofen, a type of non-steroidal anti-inflammatory drug (NSAID) used to reduce pain, fever, and inflammation. GasX is an over-the-counter medication used to relieve gas and bloating caused by indigestion. Both ADVIL and GasX are popular medications used to provide relief from various ailments.