Just outside Oslo there is a large peninsula called Nesodden, both nes and odde are words that still mean “promontory/peninsula” in Norwegian. The tip of that peninsula is called Nesoddtangen, adding another word for “promontory/peninsula”. It’s the point of point-point.
It goes deeper than that. It’s forks all the way down. I’ve come across references (variously spelled) to “[the] East Fork of [the] North Fork of [the] North Fork [of the] American River.” I’m not sure if that’s an official name.
In NY, there are the East Branch Croton River, the Middle Branch Croton River, and the West Branch Croton River.
Near me, there’s a Spring Street Road. There’s also a Quaker Lane in Quaker Street, NY.
I remembered something from an old Guinness Book of World Records, and found it on Wikipedia: New Brunswick has the “Lower North Branch Little Southwest Miramichi River”, which is also the 9th longest place name in Canada.
Most people don’t know that RI is officially known as State of Rhode Island and Providence Plantations
I can’t find it now, but I think there is an island in a lake on an island in a lake on Isle Royale in Lake Michigan.
There used to be a web site about recursively nesting largest islands/lakes, but I couldn’t find it. Others have jumped into the void it left, such as The Island in a Lake on an Island in a Lake on an Island. And I suspect the one you’re thinking of is on Manitoulin Island in Lake Huron, which that site covers.