The firm has paid local authorities 17m yen ($180,000; £123,600) a year for a decade for the naming rights.
It plans to turn a small public park into a park for futsal, a variant of football, and build rock-climbing facilities and skateboard ramps.
Homeless people have been moved from the park, but dozens of activists have since moved in to oppose the plan.
'Social responsibility'
Thousands of homeless people live in cardboard and plastic shelters in public parks in Japan.
Ward officials say they have helped the homeless people who had lived in the park to enter shelters or move to a nearby site.
However, activists say they will prevent local officials and construction workers from entering the park to develop it, objecting that a public space is being let to a "private company".
Nike says the project is part of its "social responsibility" work.
Construction work was originally scheduled to have started last September, but was delayed to April and has since been blocked by protesters.
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