ALBANY—Gov. Andrew Cuomo in 2013 rolled out what he said would be a “game-changer” for the ailing upstate economy, a 10-year tax break for companies that open shop in certain areas of New York.

But after a report showing the program created only 408 jobs in two years after a $50 million taxpayer-funded ad campaign, the governor is seeking to overhaul the program.

His executive budget proposal, released Tuesday night, proposes changing the criteria to qualify for the tax break and renaming the initiative. While the basic model remains intact—a tax break for companies moving to certain zones in the state, particularly near college campuses—it would now target companies five years or younger with 25 or fewer employees.

The new proposal would also create uniform criteria for qualifying, rather than region-specific criteria, focus less on specific job-number goals for the companies involved, and offer an additional tax break for the companies that produce more jobs.

The name—Start-Up NY—has also been stripped from the program under the proposal and replaced by “Excelsior Business.”

If enacted, Excelsior Business would join a number of initiatives led by Mr. Cuomo branded “excelsior”—“ever upwards,” in Latin—this year, including state scholarships and a book laying out his priorities. The Second Avenue Subway, an initiative the governor was closely involved in, also has “Excelsior” engraved on a wall.

A spokesman for the Empire State Development Corp., the state agency overseeing economic development, said Wednesday that the basics of the Start-Up program would remain the same under Mr. Cuomo’s proposal but “adjustments…are based on feedback from businesses.”

The idea must be approved by the state Legislature, where some lawmakers in both parties have called for ending the tax program altogether, saying it was costing the state tax revenue without creating enough jobs to justify itself.

Mr. Cuomo also came under fire over ads promoting the program that critics said promoted him as well. His office has pointed out he didn’t appear in the ads and said they were intended to show New York state as business-friendly. They have also said the program will create more jobs over time.

Sen. John Flanagan, the Republican majority leader, said he is still reviewing the proposal but expressed skepticism about the changes. A spokesman for Assembly Speaker Carl Heastie, a Democrat, didn’t comment.

Kenneth Girardin, an analyst for the policy think tank Empire Center, said it wasn’t clear the proposed changes would improve the program as a jobs creator but that it was a start. “What they have done here is accept defeat with Start-Up NY,” he said, ”and that’s the first step towards talking about real ways to improve the upstate economy.”

© 2017 Wall Street Journal