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The Guinness Book of World Records says:
The first known cat with a name was called Nedjem meaning 'sweet' or 'pleasant' and dates from the reign of Thutmose III (1479-1425 BC).
This is also mentioned in the book The Cat in Ancient Egypt, which adds that Nedjem was found in the tomb of a nobleman named Puimre and that unlike dogs, naming cats in ancient Egypt was uncommon.