Joseph P. Gamble was recently named president of Group Hospitalization Inc., the area Blue Cross plan. He replaces Donald S. Farver, who will retire in late December after a 12-year term as president.

Gamble's current position as executive vice president will be assumed by Benjamin W. Giuliani, who has served as senior vice president of finance for Group Hospitalization Inc. since 1979.

Gamble, a native Washingtonian, joined the organization in 1957 as assistant controller. He went on to become controller in 1959, assistant director in 1963 and senior vice president in 1969.

Giuliani followed Gamble as controller after joining Group Hospitalization Inc. in 1961 as senior accountant. He assumed his current position in 1969.

The organization's board of trustees also elected Thomas R. Harrison as its chairman. He will replace Harold D. Fangboner, who died in August. Harrison, who has been a member of the board since 1975, is vice chairman of the National Permanent Federal Savings and Loan Association. He also is a member of the board of directors of the Hospital Council of the National Capital Area.

LaSalle D. Leffall Jr., professor and chairman of the Department of Surgery at Howard University College of Medicine, will replace Harrison as vice chairman of the board.

Group Hospitalization Inc. serves about 1.4 million subscribers in the Washington area. Benefits of $ 250 million were disbursed in 1980. The organization also paid $ 169 million last year in Medicare Part A benefits.