IN a pop quiz, most Americans would probably confuse his name with that of a Bulgarian tennis pro or perhaps a Swedish auto magnate. But very few residents of the Buckeye State would make that mistake. Ohio Gov. George Voinovich was reelected in 1994 by the highest margin of any Republican chief executive (72 percent) - a record this century within the state. That achievement, and an approval rating that has stayed above 62 percent for more than two years, has put Mr. Voinovich on most lists for Republican vice presidential nomination or possible Cabinet post. ''His astonishing popularity within a populous, industrial state, is making Voinovich a major attraction in one of the key, Presidential battlegrounds,'' says William Schneider, a political analyst at the American Enterprise Institute. No Republican has ever made it to the White House without carrying Ohio. President Clinton, too, will find it difficult to get reelected without the state's 23 electoral votes. Often mentioned in the same breath as other governors from the Midwest who have pushed the Republican Party in new directions - such as Michigan's John Engler and Wisconsin's Tommy Thompson - Voinovich is less well-known and harder to pigeonhole. Part of the reason is what some call a ''studiously non-ideological'' approach that has steered clear of the standard GOP agenda - an independence that, at times, has put him at odds with his own party. ''Voinovich is not a great ideological leader and the national Republican Party is in a great ideological mood,'' says Mr. Schneider. Noting Voinovich's surprising lack of national profile despite being governor since 1991, Schneider adds, ''Public and politicos alike want to know, 'what has [Voinovich] done to earn such praise?' How has he done it?'' Roll-up-the-sleeves manager By most accounts, Voinovich is a low-key, roll-up-the-sleeves, fiscal manager. His resume over 30 years is cluttered with public-service jobs: state assistant attorney general, Ohio House member, county commissioner, county auditor, lieutenant governor - as well as chairman of the Council of Great Lakes Governors and several national task forces. Elected to his first term in 1990, he likes to quote what has become a favorite Republican mantra: ''The new realities dictate that public officials are now judged on whether they can work harder and smarter and do more with less.'' ''In his first four years, he came in and did what people wanted him to do, which was get a handle on the size and scope of government and rein in spending,'' says Lee Leonard, chief statehouse correspondent for the Columbus Dispatch. He has held the $33 billion budget to its lowest growth-rate in 40 years while raising state support for several programs that help children, such as Head Start, as well as some family and elderly programs. Public/private partnerships and volunteerism have been central themes of his frugal tenure, as they were when he was mayor of Cleveland. Clearly Voinovich has benefitted from a buoyant economy. Unemployment in Ohio is at a 20-year low. The state has ranked first in the nation for new and expanded business facilities the past two years, and first in the number of companies involved in export. Supporters would attribute at least some of this good fortune to the governor. He has granted tax breaks and other business incentives tied to the creation of jobs. The governor has whittled away at the number of state agencies, personnel, and cabinet positions. He has cut welfare rolls by 147,000 - a move that puts him in line with what several other GOP governors have done but has angered advocates for the poor. ''He is a non-ideological, results-oriented pragmatist,'' says Linda Bennett, a political scientist at Wittenberg College in Springfield. In a state somewhat divided with liberal Democratic bases to the north and east and conservatives to the south and west, Voinovich has tried to ply the middle ground by splitting positions on volatile issues such as welfare, affirmative action, and abortion. Affirmative action He hasn't been able to avoid controversy, though. He has angered GOP conservatives by stating that, as a son of immigrants who were aided by affirmative action laws, he could not support moves to roll back such laws. He also went along with a tax increase his second year in office to avoid what he considered disastrous cuts in education programs. That move, coupled with a proposal earlier this year to overturn a citizen-rejected tax on soda beverages, prompted the Wall Street Journal to tag him ''the nation's premier GOP tax raiser.'' Undeterred, the maverick Republican has taken on antitax groups on another front: He is opposing attempts to require a two-thirds (super-majority) vote for any tax increase in the state. He calls such a stricture ''un-American'' because it runs counter to the principle of majority rule. ''He cannot fairly be labeled a tax-raiser,'' says Leonard, the journalist. ''But because he is the kind of guy who might if he thinks it's necessary, that's what makes conservatives so mad.'' Shift to workfare On welfare, Voinovich signed legislation August 15 that moves Ohio, like other states, in the direction of shifting recipients from welfare rolls to payrolls. Among other things, it requires unmarried, unemployed welfare mothers to undergo job training and education to receive cash benefits. Benefits will be restricted to three years over a five-year period. ''The time-limit compromise we reached creates a series of reasonable protections for vulnerable families,'' Voinovich said in a 90-minute interview here. ''We send a message to recipients that welfare cannot be a way of life, but at the same time we ensure that families will have the opportunity to receive the supports they need to become independent.'' Voinovich has run into opposition from elements of the education establishment for his support of school vouchers. But he has won kudos for reform of workers' compensation laws, and for privatizing state liquor stores. Conservative complaints Conservatives complain that Voinovich has made too many overtures to business without assuring that jobs have materialized as a result.''He claimed the last administration was bought and paid for by lobbyists,'' says Leonard, ''but he still accepts $25,000-plate fundraising money while he says with a straight face that donors aren't getting favorable treatment.'' That galls the press, Leonard says, but hasn't rubbed off on the average voter. Voinovich knows he is attracting national attention, but denies reports that he is jockeying for national recognition with such GOP governors as William Weld of Massachusetts and Christine Todd Whitman of New Jersey. As early as January he was the first major figure to support Sen. Bob Dole (R) for President - while heading the Kansas Senator's Ohio campaign. But he dismisses himself as a serious candidate for vice president. ''I really believe that with my candor and the way I handle things, it does not fit in with certain people's thoughts about the party,'' he says. ''I can't pass the litmus test I think many are going to require of someone who is going to be VP.'' Just as well, say several analysts here, holding that Voinovich's fiscal and management skills are better suited to a Cabinet or other position rather than such a political role as No 2 to the President. Still, there are other ways Voinovich could end up in Washington. The betting here is that he will run for US Senate, taking aim at the only office he has run and lost for - a closely contested race against Howard Metzenbaum in 1988.