Verdia L. Haywood, a 33-year-old budgeting expert, was named yesterday to a new top Fairfax County government job, becoming the first black to hold a high position with the county, which is under federal court order to cease race and sex discrimination in hiring and promotion.

Haywood, who now serves as executive assistant to County Executive J. Hamilton Lambert, will assume the new job of deputy county executive for public service June 1. The job pays $51,000 a year, more than $10,000 above Haywood's present salary.

Haywood was named to the job by the County Board of Supervisors, who also -- as expected -- appointed Police Chief Richard A. King to the new post of deputy county executive for public safety.

Board Chairman John F. Herrity said that while he believes strongly in affirmative action, Haywood's appointment "was strictly a merit promotion . . . It had nothing to do with race or with the problems the county has had with the courts or the Justice Department." Six weeks ago, a U.S. District judge in Alexandria ruled against the county in a discrimination suit filed by the Justice Department in 1978.

Justice based its charges on 1977 statistics that showed that only 5.6 percent of 7,000 workers employed by the county at the time were black, compared to at least 24 percent of the work force in the metropolitan Washington area.

In April 1979, U.S. District Court Judge Albert V. Bryan Jr. largely rejected the Justice Department's case, but the 4th U.S. Circuit Court of Appeals sent the case back to Bryan, ruling that the judge had failed to give proper consideration to some of the evidence presented against the county.

The charges were vigorously contested by the county, and Board Chairman Herrity sent letters to President Reagan and Attorney General William French Smith early this year urging them to drop the matter on the basis of Reagan campaign pledges to end harrassment of local officials.

Then, on March 31, Bryan reversed his earlier ruling after hearing three days of testimony.

County Personnel Director Cornelius J. O'Kane said yesterday that while Haywood's promotion was a matter "of sheer ability," it is "a continuation of a pattern of blacks and females rising in the management structure."

O'Kane said that currently more than 11.4 percent of the approximately 5,800 full-time county workers are minorities, and that the majority of those are blacks. O'Kane's figures, unlike those used in the Justice Department's 1978 suit, included only full-time employes.

The county's population is about 560,000, 5.9 percent of whom are black, according to county figures.

Haywood said yesterday that even though he will become the highest black official in Fairfax County, he does not intend to use his position to "be a voice for any particular group. I will be a voice for human services in the county, for whoever is in need.

"This appointment is not of a racial nature," Haywood said. "I would have been inclined not to accept it if I thought it was."

Haywood came to the county in January 1978. He holds a bachelor's degree with honors from Alcorn State University in Mississippi and a master's degree in public administration from the University of Illinois.

In 1971 he was hired as a management intern by the City of Richmond and worked his way up to senior budget analyst concerned with preparation and oversight of the budgets of Richmond's human services agencies.

As assistant to county executive Lambert, Haywood has done everything from ordering dinner for all the supervisors during late meetings to communicating board instructions to county agencies. He has worked extensively on Human Services issues during the last two years, and has been a member of the Social Services Board, which has operating responsibility for the county Department of Social Services.

The promotion of Col. King, the current police chief, to the newly created position of deputy county executive for public safety will give him a $6,000-a-year raise to $62,284 and responsibility for both the police and fire department operations. Deputy Chief Carroll Buracker, 38, will serve as acting police chief until a replacement for King is named.

King, 50, who came to the department in 1955 and was named chief in 1975, earned a reputation as a skilled and effective administrator who staunchly defended his men against community and media allegations of police misconduct and excessive use of force. He is also credited by many with deflecting pressure for a civilian police review board by creating citizen advisory commissions with sharply limited powers.

Both Haywood and King's new positions were created by the county board two weeks ago as part of a county management reorganization plan.