Republican senators vying for re-election this year have had to contend with a cratering economy and an unpopular president. Senator Jon Husted of Ohio appears to have an additional challenge: Even some the state’s most devoted conservatives don’t know who he is. Mr. Husted’s Democratic opponent is Sherrod Brown, a fixture in Ohio politics since the 1970s, who lost his Senate seat two years ago. Mr. Brown’s renown has become something of a liability for the sitting senator, who needs the state’s MAGA-friendly Republican base to care enough about the seat to vote in a year when President Trump is not on the ballot.

But being perceived as the challenger may also benefit Mr. Husted at a moment when voters are struggling economically and don’t think Congress has done enough to help. With polls showing Mr. Brown and Mr. Husted in a tightening race, the Republican’s campaign has leaned into the misconception, spending millions of dollars on ads that refer to his opponent as “Senator Sherrod Brown.”

One Republican strategist in Ohio said the campaign was intentionally casting Mr. Brown as the incumbent, a rare opportunity amid dismal Republican approval ratings to harness anger at the status quo. Mr. Husted was appointed to the Senate two years ago, when JD Vance vacated the seat to become vice president. Quality polling on Ohio is limited, but one poll found that nearly a quarter of voters believed Mr. Brown was the incumbent. The high-stakes race has become one of the most expensive in the country, with nearly $400 million of spending on advertisements, according to Ad Impact. So far, Republicans have outspent Democrats by more than $75 million.