The Education Department yesterday announced that it has begun giving the Selective Service System the names of students who apply for federal college aid money. The names will be checked to see that eligible males have registered for the draft at their local post offices before they receive any federal student aid.

Education Secretary William J. Bennett announced the agreement at a news conference attended by Maj. Gen. Thomas K. Turnage, director of the Selective Service System, and Rep. Gerald B. Solomon (R-N.Y.), sponsor of a law that prohibits students from receiving federal college aid unless they register for the draft.

The law was passed in 1982, but this marks the first time the department has turned over names of students to the Selective Service System.

Over 5 million students apply each year for low- income Pell grants, and about 2.5 million receive them. The department will first turn over the names of last year's applicants, followed by a list of this year's Pell grant recipients. From then on, the department will turn over the list of applicants each October, and a list of Pell recipients three times each year.

But the new program will for the time being leave untouched most of those students who receive the popular guaranteed student loans and who do not apply for Pell grants.

Guranteed student loans are administered through private lending agencies, and a department official said they are trying to work with those lenders to get the names of all loan applicants.

The national draft was abolished in 1973, but the Carter administration began requiring draft registration following the Soviet invasion of Afghanistan in 1979.

At the news conference, Bennett quoted President Theodore Roosevelt, who said, "The first requisite of a good citizen in this republic of ours is that he shall be able and willing to pull his weight."

Bennett added that "one of the ways in which college students can pull their weight and fulfill their responsibilities of citizenship is by standing ready to defend their country in time of need."