Gov. Charles S. Robb today named Sue Fitz-Hugh, a legislative aide with close ties to the state's conservative independents, as the state's top elections official, capping a fierce struggle among his supporters.

The position of secretary to the Board of Elections is considered among the most politically sensitive appointments Robb has made, forcing him to choose among two rivals promoted by Democratic Party officials and members of the legislature.

The appointment has been closely watched as well by liberals and black activists who have long viewed the outgoing secretary, Joan Mahan, as an overly zealous enforcer of some of the state's more restrictive -- and controversial -- voter registration policies.

In naming Fitz-Hugh, a 39-year-old former office worker in the conservative "Virginians for Robb" committee, Robb acted to defuse potential criticism. First, he reappointed Earl Wayne Davis, a 71-year former AFL-CIO official whom he had named as the first black member of the elections board last year, as board chairman.

Next, Robb declared that boosting the state's voter rolls would be among Fitz-Hugh's prime responsibilities. "I have talked with Sue about the need to significantly increase both the number and percentage of Virginia's registered voters," Robb said. "Our state is said to rank among the lowest in the nation in the percentage of registered voters."

Despite Robb's failure to support actively any of the 10 bills to boost registration before the General Assembly, the statement and reappointments won support from blacks in the legislature. State Sen. Robert Scott (D-Newport News) said he didn't know that much about Fitz-Hugh's views, but "taken the two appointments together, I'm satisfied."

Also named by Robb as the Republican member of the three-member board was Albert G. Cook III, the general manager of Colonial Parking Inc. in Washington and a former Alexandria city councilman.

The jockeying over the replacement of Mahan, a former Fairfax County Republican, mobilized much of Robb's electoral coalition. Sandra Bowen, a Richmond housewife and former Richmond Democratic chairman, surfaced as the candidate of many party regulars, including Attorney General Gerald L. Baliles.

As clerk to the Senate Privileges and Elections Committee, Fitz-Hugh was backed chiefly by her boss, Senate Clerk Jay Shropshire, who lined up support from Majority Leader Hunter B. Andrews (D-Hampton) and other senators on her behalf. She was chiefly known, however, for her ties to the "coalition" -- a loose network of conservative businessmen who swing back and forth between the state's political parties. Fitz-Hugh is the daughter of retired Norfolk banker W. Wright Harrison.

Mahan, who was appointed to the job in 1971 by Gov. Linwood Holton, left the elections board effective today to become executive secretary of the Virginia Bar Association.