American Telephone & Telegraph Co. yesterday named Charles L. Brown, 55, as president and chief operating officer, effective April 1.

Brown will succeed William L. Lindholm, 62, who is retiring early "at his own request," AT&T said yesterday. Lindholm, former president of the Chesapeake & Potomac Telephone companies here, has been chief operating officer since 1972 and president since last year.

AT&T board chairman John D. deButts said of the surprise Lindholm decision: "His capabilities and talents will be missed, but he wishes to return to Texas, his home for many years . . ." Lindholm started his Bell System career in 1936 at Southwestern Bell in Dallas but probably could not have risen any higher at AT&T because he is older than the current chairman.

Currently vice chairman and chief financial officer, Brown is a graduate of the University of Virginia.

AT&T also named William S. Cashel Jr., as vice chairman and chief financial officer succeeding Brown James E. Olson, president of IIinois Bell, as executive vice president; Charles Marshall as president of Illinois Bell and William G. Burns as vice president and treasurer of AT&T to succeed Marshall.

Olson will be in charge of AT&T's Washington office.