Robert B. Costello has been named by President Reagan to fill a key vacancy in the Defense Department hierarchy, undersecretary of defense for acquisition, and may face contentious confirmation hearings in the Senate.

Costello would replace Richard P. Godwin, who resigned earlier this month in what he said was frustration over the Pentagon's bureaucracy and his inability to forge reforms in its purchasing practices.

Costello, 61, is a former executive of the General Motors Corp. who has served as the Defense Department's assistant secretary for acquisition and logistics since last year. In that job, he reported as a top deputy to Godwin.

The post of undersecretary for acquisition was created a year ago by Congress with the goal of centralizing the procurement of new weapons in one office. Congress has reasoned that such centralization might help eliminate the duplication that now exists among the four armed services as they develop and buy weaponry.

Godwin, in appearances before two congressional committees earlier this week, said he had quit the job because he did not believe the department was serious enough in its efforts to end wasteful practices.

"My decision to resign rested upon my judgment that we were not prepared to move ahead with a new acquisition system," he said.

Reagan also has nominated Air Force Maj. Gen. Donald J. Kutnya, 53, to head the Air Force Space Command. If confirmed by the Senate, Kutnya would become a lieutenant general in assuming the new post. He will replace Maj. Gen. Maurice C. Padden, who is retiring Nov. 1.