Stephen Joel Trachtenberg, an outspoken advocate of private colleges, was named president of George Washington University yesterday and promised to raise the institution's "presence and influence."

Trachtenberg, 50, headed the University of Hartford in Connecticut for 11 years. An active Democrat and sharp-tongued critic of U.S. Education Secretary William J. Bennett, he succeeds Lloyd H. Elliott, a low-key, nonpolitical administrator who will retire in June after 23 years.

Trachtenberg was chosen unanimously both by the GWU board of trustees and by a 13-member search committee that included trustees, faculty members and alumni and student representatives.

In a statement after yesterday's board meeting, Trachtenberg said he would seek to "balance" the university's "devotion to teaching, research and service . . . with a powerful involvement in national and international affairs."

Last month, Elliott refused to allow the university's gymnasium to be used as a press center for the summit between President Reagan and Soviet leader Mikhail Gorbachev, saying it would disrupt classes.

Trachtenberg declined to comment on Elliott's decision directly, but remarked in an interview, "No pain, no gain." Last week in an interview with the Hartford Courant, Stillman B. Brown, chairman of the University of Hartford Board of Regents, said Trachtenberg probably would have agreed to the press center. "If Steve had been there, it would have become the Gorbachev-Reagan-Trachtenberg summit," Brown said.

A Hartford University press release credited Trachtenberg with tripling the school's endowment, doubling its dormitory space and upgrading its athletic program to Division I. Hartford has an enrollment of 7,500 students, compared with 18,000 at George Washington.

Elliott, 69, is the longest-serving president of any major U.S. university and has spearheaded a massive building program that spread George Washington's campus over much of Foggy Bottom.

At Hartford, Trachtenberg has been a strong advocate of government aid to students at private colleges and has argued that state colleges subsidize wealthy students through low tuition. He also has accused Bennett of "scapegoating" and using "hate-filled language" for saying that American colleges are often too costly and ineffective.

In 1984, Trachtenberg helped draft the nominating speech for vice presidential candidate Geraldine Ferraro.

Born in Brooklyn, N.Y., Trachtenberg graduated from public high school there and attended Columbia University and Yale Law School. He worked as a U.S. Office of Education aide in the Johnson administration and later was a vice president of Boston University.

Trachtenberg's wife Francine is an art historian who works as director of capital projects at the University of Hartford. They have two sons, ages 9 and 12.

Trachtenberg is active in campus Jewish organizations, serving on the national board of the Hillel Foundation. He is the first Jewish president of GWU, whose student body is about one-third Jewish, one of the highest proportions in the country, according to Hillel.

Trachtenberg declined to say what his salary will be, but several sources familiar with his hiring said he will be paid more than $100,000 annually.