Government Employees Insurance Company turned over to the D.C. Board of Elections and Ethics yesterday its reconstructed computerized register of voters in the city -- a register that lists 290,804 names, including 51,537 that were dropped from the computer rolls following the November 1980 general elections.

Geico vice president Alvin Kaltman told the board that the reconstructed register still did not represent an exact count of voters in the District of Columbia. That would have to be produced through the board's own efforts, picking up where Geico left off, he said.

Geico estimated that the final result would be somewhere around 293,000. Contributing to this increase would be some of the 9,500 names that were separated out of the city's computerized lists as duplicates, but which may prove to be those of legitimately registered voters.

Geico turned over its final report to Elections and Ethics Board Chairman Albert J. Beveridge III in an hour-long ceremony that included a slide show and news conference at Geico headquarters in Chevy Chase.

Teddy Filosofos, who took charge of the city's troubled elctions system recently after he was hired from a similar position in Erie County, N.Y., said that while the Geico register still was incomplete, "it's the most complete yet."

Filosofos said that the board would review the Geico figures to produce by the Sept. 14 primaries a list of all voters who have registered in the city since 1980.

Geico's final figures were reconstructed from 237 tapes provided by the board.