MAN IN THE NEWS; CHIEF OF STATE'S PRISONS: THOMAS ALOYSIUS COUGHLIN 3d

''There's no doubt about who's in charge - he's the captain,'' a correction union leader said yesterday of Thomas Aloysius Coughlin 3d, the New York State Commissioner of Correctional Services.

The union leader, John Burke, who was present at the Ossining Correctional Facility during the long hours of negotiations to obtain the release of 17 prison guards taken hostage, said that watching Mr. Coughlin in action confirmed his admiration. ''In 25 years,'' said Mr. Burke, executive director of the council representing 14,000 state correction and police officers, ''he's the best I've ever seen. I thank God that some of the commissioners in the past weren't in charge.''

Others, including some inmates, share at least part of that assessment. And close associates say that the 44-year-old Mr. Coughlin (pronounced COG-lin) will be staying on under Governor Cuomo as head of the state's 32-prison network now housing 28,413 inmates - more than 12 percent over the system's capacity. Holding System Together

''The biggest testament is not just how the incident at Ossining is resolved, but what has been happening elsewhere,'' said Meyer S. Fruchter, the state's deputy director of employee relations, who headed the search committee of former Gov. Hugh L. Carey that picked Mr. Coughlin for the job three and a half years ago. At that time, Mr. Fruchter said, ''the system was coming apart at the seams.''

''Now it's stretched to the seams,'' he continued, ''but it's not coming apart.'' Mr. Coughlin himself took a grim view of the prospects shortly after taking over. ''The situation for the next few years is going to be extremely tense,'' he warned.

That the badly overcrowded facilities have not been racked by more disturbances is attributed by some to Mr. Coughlin's willingness to hear inmate grievances. He sits down with inmate committees, and solicits letters from inmates and reads them. At the same time, he has ministered to the concerns of correction officers, sometimes arriving at prison gates at 5 A.M. to greet them as they change shifts and to listen to their complaints.