New Zealand is named after a Dutch province, and that province is named for the sea.
The story begins in 1642. The Dutch explorer Abel Tasman sighted the western coasts of the islands. According to Te Ara, he called the land Staten Landt, possibly linking it to a place of that name near the southern tip of South America. That link was soon ruled out.
Back in the Netherlands, the mapping caught up. Te Ara says that in 1643 Hendrik Brouwer showed the other Staten Landt was a small island, not part of a southern continent. Joan Blaeu, cartographer to the Dutch East India Company, then gave the land the name Nieuw Zeeland, Nova Zeelandia in Latin. Wikipedia says Dutch cartographers renamed it in 1643 or shortly after. Nova Zeelandia is the Latin form of the Dutch Nieuw Zeeland.
They named it for the Dutch province of Zeeland. History.com describes it as a low-lying coastal area, and Mental Floss says it is made of islands and its name means "sea land."
English speakers later took up the Dutch name. History.com says Cook and later British arrivals kept it in an anglicized form after his voyages in the 1770s. Te Ara adds a caution: Cook did not name the country himself. He wrote down Māori names for the two main islands as he heard them.
Later dissatisfaction that the name was foreign never led to a change. Te Ara also notes that the phrase "Aotearoa New Zealand" is commonly used today. It says the Geographic Board cannot change the country's name, though it encourages using original Māori place names on official maps.
So the answer to "why Zeeland?" is mostly a mapmaker's choice. A Dutch cartographer picked a Dutch province for islands on the far side of the world, and the name outlasted the Dutch interest in them.