The last thing Donald L. Dotson wanted when he became chairman of the National Labor Relations Board was to push the tiny, independent agency into the spotlight.

The lanky former assistant secretary of labor for labor-management services had wanted the agency to adopt a lower profile and stay out of disputes that could be resolved without the federal government's help.

Yet, in the three months since he took over, the agency has been enveloped in controversy.

Last month the board caused an uproar when it announced it was "reclaiming" most of the litigation and enforcement powers that the agency's quasi-independent general counsel had assumed since 1955.

Among other things, the board's decision gave Dotson control over the hiring, firing and promotion of all agency attorneys and put Hugh L. Reilly, the board's personal solicitor, in charge of agency appeals.

The fact that Reilly, who accompanied Dotson from the Labor Department, had once worked for the National Right to Work Committee, fueled rumors that Dotson was about to lead a purge of liberals at the NLRB.

Dotson has tried to defuse the fears by issuing a memo that assured employes that, among other things, no political maneuvering was in the works. He also asserted that he didn't care if enforcement attorneys wore blue jeans to work as had been alleged in some news accounts.

But some employes are still upset. The professional association that represents the agency's 80 enforcement attorneys complained formally to Dotson this week, demanding that he apologize for criticizing agency attorneys whom he has described as "cocky" and "arrogant."

In retrospect, Dotson said that he and other board members should have issued a news release when they reclaimed the general counsel's powers. Such a move might have been out of character for someone who shuns publicity and says he dislikes interviews because he says he is often misquoted--but who wouldn't let a reporter use a tape recorder.

Associates describe Dotson, 44, as a "private," "stern," "disciplined," "no-nonsense attorney" who likes to read history books, garden and ride his Triumph motorcycle on weekends.

He does not appear to be a self-promoter. He says all of the jobs he has held since becoming an attorney, except one, were unsolicited--and that includes the chairman's post. He also claims no political ambitions; he was registered as a Democrat when the Reagan administration offered him a job.

It first approached him about a seat on the NLRB, which he rejected, saying he preferred to remain chief labor attorney for Wheeling-Pittsburgh Steel. He later accepted the Labor Department job because it "sounded challenging." To this day, Dotson claims he doesn't know who put his name forward, but he did change his party affiliation before moving to Washington.

He was considered to be such a noncontroversial nominee to the Labor post that the Senate Labor and Human Resources Committee approved his nomination without formal hearings.

He went straight to work for the NLRB after graduating from Wake Forest University's law school. He remembers a corporate attorney telling him during his first case that he considered NLRB attorneys among "the sorriest people on the face of the earth."

He handled a variety of labor disputes and served as president of the local NLRB employe union during the next five years before Westinghouse Electric Corp. offered him a job at its Pittsburgh headquarters. Two years later, Western Electic Co. lured him away and the following year, Wheeling-Pittsburgh Steel Corp. did the same.

At the Labor Department, Dotson enforced the Labor-Management Reporting and Disclosure Act and Employe Retirement Income and Security Act. He dramatically increased the number of unions that were audited.

Dotson said he reluctantly agreed to take the NLRB chairmanship late last year after it became clear that Reagan's first choice, John Van de Water, was not going to win Senate approval. AFL-CIO President Lane Kirkland expressed "grave reservations" about Dotson in a letter to the Senate, but the administration pushed his nomination through the committee without a dissenting vote.

Dotson says he is trying to bring a sense of professionalism to the board and that the first step is to bring agency attorneys into line. They must learn, he said, that they are not "independent policy makers . . . . They are the board's attorneys."

The next step, he said, is for the board to adopt a more reasonable view of employer-employe disputes, which means giving the two sides time to negotiate without outside interference.