When Lee P. Brown arrived at city hall this morning to be sworn in as Houston's police chief, his name was already installed on the lobby's roster of public officials. But later, when he got to the police headquarters that houses many of his sharpest critics, there was no sign of him in the building directory.

It was another small reminder to Brown, the former public safety commissioner in Atlanta who led the investigation into the murders of 28 young blacks, that while he may be the darling of the mayor's office he has not tamed an often unruly Houston police department.

Brown's friends in Atlanta gave him a pair of cowboy boots as a going-away present, but there was no hint of the cowboy in Brown today as he coolly maneuvered his way through breakfast with Mayor Kathy Whitmire (who has clashed with the police department during her three months in office), a headquarters tour, two roll calls and a news conference.

"There is certainly a need for stability," Brown said, "and I would hope that I'll be the one to provide the stability." Brown said he hoped to turn Houston's police force into a model for the rest of the country.

There were smiles all around today, but the problems Brown, 44, must confront are grim. The first black chief in the city's history, he assumes command of a 3,200-member force, spread thin by population growth and geographical sprawl, that suffers from morale problems and whose leaders openly opposed Brown's nomination. The city council approved Brown's nomination 11 to 3, despite lobbying against him by the Houston Police Officers' Association.

"The people here were not against Lee Brown," said acting chief John F. Bales said. "There were people here who believed that the chief should come from within the police department."

The department has a lingering reputation for brutality and racial insensitivity. The latest evidence is only a few days old: last Friday, seven officers were dismissed and six suspended for terrorizing and beating black residents of a local hotel. The off-duty officers had been drinking at an election-night barbecue. A grand jury is investigating.

In mid-April, Bales suspended an assistant chief for ignoring a stabbing outside a bar where he was drinking.

In recent years, a number of brutality cases have tarnished the police department's standing in the community. The most publicized incident came in 1977, when a young Mexican American, Joe Campos Torres Jr., was arrested during a barroom brawl. Police later took him to a nearby bayou and shoved him over the embankment into the water, where he drowned.

There were other incidents during that period, and while the situation has improved, the problems have not been eliminated.

"We've had a reputation because of a very few number of incidents," Bales said. "Every city has something like that from time to time. I'm not trying to blow that off and say we should expect it, because we don't expect it. We don't condone it. But we're also dealing with human beings."

A study by the International Association of Chiefs of Police released last fall showed that the number of fatal police shootings in Houston between 1975 and 1979 was 5.8 for every 1,000 officers, more than twice the national average.

The department has had a poor record of recruiting minorities, although it is improving. About 8 percent of the force is black and about 8 percent Mexican American. In early April, a black officer was promoted to lieutenant for the first time.

"There has been a feeling in the minority community that joining the police department is not an honorable profession," said Mayor Whitmire.

This is not the first time Brown, who holds a doctorate in criminology, has come into a troubled department as an outsider. In Atlanta, he took over an undermanned force still demoralized by fallout from a promotion cheating scandal.

He helped solve the spate of racial discrimination lawsuits filed against the department by black and white officers, breaking a five-year hiring and promotion freeze. He also earned the support of the downtown business establishment.

"He helped solve much of the internal strife and racial troubles that plagued the department when he came here," said Atlanta public safety commissioner George Napper, former chief under Brown. "He leaves an important legacy that we will build on."

But it was his leadership in the investigation into Atlanta's child killings that earned Brown the community's lasting respect, and which brought him to the attention of the outside recruiting firm working for Whitmire in Houston.

During the 22-month trauma of the child killings, Brown rose at 6 a.m. and went to bed at midnight. From the banks of the Chattahoochee River, where many of the bodies were found, to community meetings where he tried to reassure a frightened public, he showed little emotion, earning various nicknames like "Iceman," "the Sphinx," "No Rap."

He held information close and spoke at news conferences in a bureaucratic jargon that confounded reporters and prompted a defense attorney to ask him at the trial of Wayne B. Williams if he spoke English. "I have for some years," he replied.

But his skillful handling of the investigation, which resulted in Williams' conviction in the deaths of two blacks, made him a hero by the time he left for Houston.

Now he is Whitmire's chief--if not yet the department's. Whitmire and the police force view one another with suspicion. In March she told the Houston Chronicle she believed there was corruption in the department. Later she claimed to have been quoted out of context and has sought to mend fences, but many officers have not forgiven her.

Whitmire said she hired Brown, who submitted a 31-page resume, because of his record as a good manager. "He has a broader range of experience than anyone who's spent a lifetime in Houston," she said. "The advantage to an outsider is that he brings in new ideas and has no ties to any of the factions."

Said his friend, Atlanta city councilwoman Carolyn Long Banks, "In Houston, he'll bring the kind of firmness and fairness the police department hasn't seen before."