The two crossword solutions for the term DIAMOND NAME are HOPE and LIL. HOPE is a four-letter word that is often used to express a feeling of optimism or desire for a certain outcome. It is also the name of a diamond owned by the HOPE family, which was discovered in South Africa in 1867 and is now on display at the Smithsonian Institution in Washington, D.C. LIL is a three-letter word that is often used as a nickname for someone named Elizabeth or Liliana. It is also the name of a diamond owned by the Oppenheimer family, which was discovered in South Africa in 1964 and is now on display at the De Beers Diamond Museum in London.