The usual name was the Brooklyn Home for Children. The 1925 edition of the "American Medical Directory" gives its address as 217 Sterling Place, Brooklyn.
"The National Union Catalog: Pre-1956 Imprints" treats the home under its earlier name : Brooklyn Industrial School Association and Home for Destitute Children.
A book published in 1986 contains a list of adoption agencies, including the Brooklyn Home for Children, 67-35 112th St., Forest Hills (boro of Queens) NY 11375; phone 718-263-0740.
In 1992, a newspaper titled New York Newsday printed a legal notice about a child; it contained the new name of the home---Forestdale, Inc. However, this name may refer to the institution, not the adoption agency. At one time, the home accepted referrals from the Federation of Protestant Welfare Agencies. I have no information about the home's records.
Reg Niles