As the thread title asks, what is the earliest name that has been documented in writing? A Sumerian name, perhaps?
The most recent episode of Cosmosclaimed that a Princess Enheduanna was the first to contemporaneously sign her name to her works. She lived in the Sumerian city of Ur circa 2280 BCE.
There may be other instances of names that pre-date that of Enduanna, though the written record may have been made long after the death of the individual. Such is the case for some of the names of pharaohs from the early dynastic period of Egypt.
Ka, a predynastic Egyptian pharaoh who was around in the 32nd century BCE. He had a predecessor, Iry-Hor, who would of course have the stronger claim, but whose historicity is uncertain. (Although I note that the OP doesn’t specify that the name has to be of a historical place or person; presumably the name of a mythical place or person is still a name, and can qualify within the terms of the OP.)
Ka is documented in inscriptions on vessels and other artifacts.
There are, of course, cities and other settlements that are much older than Ka or Iry-Hor. Presumably they had names. But I don’t know if we know what any of those names were.
This question has been posed in several prior threads, for examples:
What is the oldest proper name?
First historical individual
Who is the oldest probably real person we know the name of?
Who is the earliest historical figure?
Oldest real human with a name
Who Was the First Documented Person?
The Oldest Name
Enmebaragesi, who lived before Gilgamesh, was a popular choice.
There are some much earlier Egyptian Pharaohs if you allow glyph names whose pronunciation is unknown.
In this thread
Who is the earliest recorded named commoner or slave?
Shamhat, the temple harlot in the Epic of Gilgamesh, was nominated as first commoner whose name is still known.