D.C. Mayor Walter E. Washington yesterday named Bettie J. Robinson, the acting director of the city's Office of Consumer Protection, to head the agency despite political criticism that the office is mismanaged and she is incapable of leading it.

The mayor rejected last week's attack on Robinson and the agency by one of his chief foes in the Sept. 12 Democratic mayoral primary. City Council Chairman Sterling Tucker, Washington said he had "watched (Robinson) month after month take hold of a very difficult situation" in reorganizing the office and reducing its backlog of cases.

In naming the 31-year-old lawyer to the $37,000-a-year job, Washington said, "Her management has resulted in greater concentration on investigation and resolution of complaints, with quality control to make certain the best possible resolution of complaints is achieved."

At the same time, Washington lashed out at Tucker, who said last week that the Office of Consumer Protection is "the District's No. 1 (that) has all the bite of a Pekingnese.

Tucker contended the agency's backlog has increased from 639 cases to 1,847 in the first six months of 1978 and that the agency has failed to adequately serve the public. Robinson maintains, however, that the backlog had been reduced from 2,073 to 1,847 by June 30.

"I don't know where he gets his information," the mayor said of Tucker at his press conference yesterday. Mr. Tucker has once again thresbed out without adequate information. To politicize this office . . . is somewhat despicable. This undermines the effort to get the consumer cooperation."

Tucker had criticized the appointment of Robinson as acting director last March, claiming that at the time she had dismissal proceedings pending against her based on complaints from her former boss at the consumer protection office, Edith Barksdale Sloan, D.C. personnel director George R. Harrod has said there never were any dismissal proceedings against Robinson, a point the Tucker campaign now says "may be technically correct."

In a prepared statement yesterday, Tucker attacked Robinson's appointment as "an effort to stuff the whole consumer mess into a new package. I don't think that smart shoppers are going to take it (the appointment) off the supermarket shelf on election day.

"Just this Monday Robinson gave practically a point-by-point confirmation of our charges about the inefficiency in the Office of Consumer Protection," Tucker said."How much more evidence do consumers need to know that the mayor's administration is shortweighting the public?"

The mayor said he did not search for a new consumer protection chief outside the District of Columbia. "I've seen best persons come to us after nationwide searches and fall apart," he said.

Robinson has worked at the consumer protection office for nearly two years. Prior to that time she served in various capacities with the Consumer Product Safety Commission, the Neighborhood Consumer Information Center and the Model Cities Consumer Protection project. She has a law degree from Howard University.