A man with multiple identities arrested in central Pennsylvania on Monday apparently taught for two years at Towson State University near Baltimore under the name of David Arthur Gordon and used the name of a George Washington University engineering professor to lease a car and obtain a telephone credit card, Pennsylvania officials said yesterday.

Arrested as "John Doe" while walking to the classroom at Millersville State College where he taught economics, the stocky, curly-haired man known there as Peter H. Pearse had been teaching computer courses simultaneously at nearby Shippensburg State College as John Bryon Hext, according to the Pennsylvania attorney general's office. He was dismissed from Shippensburg March 10 after another professor read an academic journal containing an article written by a professor of the same name at MacQuarie University in New South Wales, Australia, whose academic credentials resembled those claimed by Hext.

Pennsylvania authorities charged the man with theft by deception, tampering with public records, forgery and false swearing after police seized 16 boxes from his apartment in Lancaster, Pa. Authorities said the boxes were filled with credit cards, resumes and other documents listing at least 13 identities.

Authorities said police also took from the apartment a telephone credit card listed to Paul Crafton of Potomac, Md., and seized a 1980 Datsun station wagon that "John Doe" drove. The car was leased to a Paul Crafton and Arthur Van B. Holland of Rockville and Baltimore, and registered to the First National Bank of Maryland, authorities said.

Pennsylvania authorities said they believe Crafton's identity is one of many "John Doe" is suspected of using.

A spokesman for George Washington University said Crafton is a professor of engineering administration who has been affiliated with the university for 20 years. Neither Crafton, Holland, nor a bank official familiar with the car ownership could be reached.

Authorities from at least six states and four nations are trying to find out just who the suspect is. "This is a very intriguing and dark mystery, who these names and people are," said Robert Gentzel, a spokesman for the Pennsylvania attorney general.

After news photographs of the bearded "John Doe" appeared, a Towson State University senior alerted newspapers that the man appeared to be the instructor who taught his upper-level finance course in the fall of 1981 under the name of David Arthur Gordon. Pennsylvania authorities said documents seized in the raid indicate "John Doe" did work at the Maryland school.

Katie Ryan, head of public affairs at Towson, which employs 768 full- and part-time instructors, said several professors in the school's Division of Business Administration, where Gordon taught accounting and finance from 1979 to 1982, recognized "John Doe" as the clean-shaven professor who left in March 1982 when the university took steps to remove him.

Gordon was hired in August 1979 at a salary of $18,000 as a temporary instructor. He was "allowed to resign" after students complained that he was frequently absent and because he failed after two years to produce transcripts of his degrees, Ryan said. He had claimed to hold bachelor's, master's and doctor's degrees in engineering from the University of London, as well as a bachelor's degreee in financial management from the University of Sheffield.

The man known as David Arthur Gordon was "very professorial," said Annette Flower, dean of Towson's College of Liberal Arts. "He gave the appearance of being knowledgeable in his subject matter and in university procedures."

The Towson State senior said Gordon was a strict teacher who gave him the only "C" in his four years at the college. He said the professor spoke in a clipped, slightly British accent and scolded students who used slang.

"John Doe," who refused to give his name, age or marital status at his arraignment on Monday, is being held in jail in Carlisle, Pa., under $150,000 bond.