To appeal to a new generation of philanthropists, the Brooklyn Community Foundation is ditching the word “foundation” and establishing itself with a new name: Brooklyn Org. Jocelynne Rainey, who took over as president of the 14-year-old grantmaker two years ago, said the name change is meant to convey that the foundation serves the residents of Brooklyn and highlights the expertise of its people, instead of suggesting a “top-down” approach sometimes taken by grantmakers. Rainey’s goal is to attract new donors and make the grantmaker — which awards about $12 million each year to a range of causes, including justice reform, housing, and health — as recognizable as the Brooklyn Museum or the Brooklyn Academy of Music.