Pan Am Corp. yesterday named Thomas G. Plaskett, the well-regarded former president and chief executive officer of Continental Airlines, to run troubled Pan American World Airways.

Plaskett, an airline marketing innovator who created several popular airline discount programs -- including frequent flier discounts -- almost immediately set the stage for a showdown on labor costs, the most critical issue facing Pan Am.

Only hours after the Pan Am board named Plaskett to replace C. Edward Acker, Plaskett wrote to the National Mediation Board rejecting arbitration of Pan Am's contract dispute with the Teamsters Union. The Teamsters are now free to strike at midnight Feb. 20, after a mandatory 30-day cooling-off period.

Pan Am, which is expected to report a loss for 1987 "significantly" more than $90 million, has sought a package of concessions that it values at $180 million from its unions. Three of the airline's unions -- the Flight Engineers International Association, the Independent Union of Flight Attendants and the Airline Pilots Association -- have agreed to concessions worth $110 million.

The other two, the Teamsters and the Transport Workers Union, have not yet reached accords with the airline.

"Pan Am is not seeking a confrontation" with the Teamsters, Plaskett said. "This company does not want nor need a strike." However, he said that the airline would continue operations in the event a strike occurs.

Pan Am typically lives off its cash reserves during the first quarter of the year -- a slack time for the tourist traffic on which Pan Am depends heavily. Industry analyst John V. Pincavage of PaineWebber Inc. said he expects the cash reserves balance will be low, given the company's expected losses. "A prolonged work stoppage could kill the goose," he said.

Reaching an accord with the unions "is the pivotal thing that has to happen" to ensure Pan Am's future, said Robert J. Joedicke, an analyst with Shearson Lehman Brothers. Joedicke estimated that the savings from the concession Pan Am is seeking would be worth $250 million.

Plaskett, 44, who has a strong background in marketing and finance, is considered one of the brightest managers in the airline industry. He served as senior vice president of marketing at American Airlines and as senior vice president of AMR Corp., American's parent. His tenure at Continental ended in July after he resigned under pressure because of differences with Frank Lorenzo, chairman of Continental's parent company, Texas Air Corp.

The resignation of Acker and vice chairman and chief operating officer Martin R. Shugrue were effective immediately, and Plaskett moved in and began working. Three senior vice presidents, including C. Raymond Grebey, the airline's labor relations chief, also resigned.

Managers in labor relations and market development will report to Plaskett in the short term, said Pamela Hanlon, a spokeswoman for the airline. Plaskett also named four new managers, including Hans Mirka, former senior vice president for field sales and services, who has been appointed executive vice president and general manager-operations.

Board member William T. Coleman Jr., who has been involved in the search to replace Acker and in negotiations with the Teamsters, is expected to continue to play a role in discussions with the labor group.

Pan Am is continuing to negotiate with the TWU, which represents mechanics at the airline.

During the past year, Pan Am has talked with several potential buyers for the airline without finding a taker. The board has met frequently over the past few months attempting to determine a future for the airline. "It's been like a soap opera," said Joedicke.