C&P Telephone President Robert E. Allen has been elected chairman of the board. He also has been named president-designate of the service company that will oversee the activities of Bell's proposed mid-Atlantic regional corporation.

Thomas M. Gibbons, C&P executive vice president for operations, succeeds Allen as president and chief operating officer of the C&P Telephone companies that serve Washington, Maryland, Virginia and West Virginia.

The Mid-Atlantic regional corporation should be fully operational by Jan. 1, 1984, the date by which AT&T must divest itself of its operating companies.

It will consist of a parent corporation in Philadelphia; the service company in the Washington area, and a cellular communications subsidiary in Basking Ridge, N.J. C&P will form the service company with Bell of Pennsylvania, Diamond State Telephone in Delaware and New Jersey Bell.

Allen joined Indiana Bell in 1957. He has been a vice president with Indiana Bell, Bell of Pennsylvania, Illinois Bell and AT&T. He became president and chief executive officer of C&P in 1981.

Gibbons began his Bell System career with Ohio Bell in 1949 and transferred to C&P in 1956. He was named executive vice president and chief operating officer of the C&P companies in 1979.