The Coromandel coast is in India. The Coromandel peninsula is in New-Zealand. Why the name Coromandel?

There's a missing link in your chain.

First of all, the Coromandel Coast is named for the Tamil word "Cholamandalam", which means "land of the Cholas", an ancient dynasty that ruled the area once upon a time. Since Europeans had a difficult time pronouncing the Tamil word, the name was basically corrupted to "Coromandel".

Second, and here's your missing link, there was a British Navy vessel named HMS Coromandel (although it was originally named HMS Malabar). In 1820, under Captain James Downie, it was sent to New Zealand to get local kauri tree logs that were used by the Royal Navy to build ships, since the wood is both long and strong, and excellent for masts and spars.

Finally, Captain Downie, being the typical European traveller that he was, named the location that he anchored in Coromandel Harbour. As the European shipping route expanded and the tree harvesting expanded up the peninsula, the town, the bay, and eventually the entire peninsula was named Coromandel. For the record, the indigenous Maori name for the peninsula is Te Tara-o-te-Ika-a-Maui.

Now, if you want to take it one step further, the Coromandel Valley, South Australia, is also named for a ship, though not the same ship, also called Coromandel. This one was built in Quebec and brought New Zealand Company settlers to the area in 1836.

https://en.wikipedia.org/wiki/Coromandel,_New_Zealand

https://en.wikipedia.org/wiki/HMS_Malabar_(1804)

https://en.wikipedia.org/wiki/Coromandel_Coast

https://en.wikipedia.org/wiki/Coromandel_Valley,_South_Australia

The name Coromandel originated in India and traveled to New Zealand by way of a British Royal Navy ship. The name is a European corruption of the Tamil word C??ama??alam (or Cholamandalam), which literally translates to "the realm of the Cholas". The Chola Dynasty was a powerful, long-ruling Tamil empire that dominated southern India and maritime trade across Southeast Asia for centuries. When Portuguese, Dutch, and British sailors arrived in India, they struggled to pronounce Cholamandalam and eventually anglicized it to Coromandel. In 1820, a British Royal Navy store ship named the HMS Coromandel (which had been renamed by the Admiralty in honor of the Indian coast) sailed into the South Pacific. Under the command of Captain James Downie, the ship anchored in a harbor on the peninsula to procure large kauri tree logs. These massive native New Zealand trees produced straight, strong timber ideal for making ship masts and spars for the British Navy. Captain Downie named the anchoring spot Coromandel Harbour. Over time, the name was adopted for the entire surrounding peninsula and the local township.