Ever controversial but endlessly game, Secretary of Labor Raymond J. Donovan, in a flurry of staff changes, social outings and meetings with business (and even labor) groups, is determined to rehabilitate himself as a functioning Cabinet official and ruin the cottage industry of rumors that he is on the verge of resigning or getting fired.

"It feels good," he said at a department Christmas party last week about his recent return to the public whirl.

To grease his comeback, he has raided the department's Occupational Safety and Health Administration for experienced staff, making Michael Volpe his personal press spokesman and Mark Cowan, a former CIA official working at OSHA, his chief of staff.

Donovan "wanted more of a 'hard' manager" to keep the department under control now that he will be away more, Cowan said.

He mentioned as "the kind of thing that shouldn't happen" the recent flap over a proposal to relax the child labor laws. "The system of review around here at that time was not effective."

Faced with a continuing cold reception from the top of organized labor, Donovan has been trying to burrow in at other levels.

He recently met with members of the AFL-CIO Appalachian Council, who were concerned about, among other things, what's happening to their Job Corps funds and to workers displaced from their jobs by economic shifts.

"It was tense at first" said Cowan, "but they finally posed for pictures with him."

YEAR IN REVIEW . . . While the department's most vocal critics (labor leaders, minority and women's groups) are releasing studies, some based on leaks, complaining about how much less this bunch is accomplishing compared with their predecessors, top Labor Department officials continue to boast about the same thing in their own papers.

In a recent report prepared for the White House as part of a periodic review, department officials patted themselves on the back for:

* Reducing the department's discretionary spending by 42 percent in 1982. This almost $5 billion reduction was touted as "the department's first since 1960" and the largest in its history, and also as exceding the "overall net government-wide reduction of $3 billion in non-defense discretionary programs."

* Legislative reforms in departmental entitlement programs saving an additional $2.8 billion in fiscal 1982, with an additional $6 billion projected for 1983.

* Regulatory relief efforts saving private industry over $1 billion a year and reducing paperwork by 25 percent.

'TIS THE SEASON . . . A touch of bureaucratic holiday whimsy was tacked to the door of Room 4512 of the department's headquarters building on Constitution Avenue last week.

It featured a printed form announcing the "Worldwide U.S. Government National Eastern Regional Mid-Atlantic District of Columbia Metropolitan Area Department of Labor Frances Perkins Building South Wing Fourth Floor Christmas Door Decoration Competition Rating Form." The artwork on the door (some crayon drawings of Santa and his deer and bits of tinsel taped on) was described on the appropriate blank as showing "subtle though distinct neogothic influence . . . . Reindeer exhibits traces of bullwinklonian style . . . ."