WASHINGTON (AP) _ President Reagan announced the appointment Thursday of Denny E. Brisley, a public affairs specialist for budget director David Stockman, as a staff assistant in the White House press office.

Meanwhile, C. Anson Franklin and Robin Gray, both assistant press secretaries at the White House, are planning to leave their posts to work for Energy Secretary John Herrington.

Franklin will be director of public affairs and Gray will be director of intergovernmental relations for the Energy Department. Kim Hoggard, an assistant press secretary since 1981, left the White House last week to become deputy assistant secretary of the Treasury for public affairs.

Miss Brisley has worked in the Office of Management and Budget since 1982. At the White House, she will coordinate the appearance of administration officials on television interview programs.