Ancient Greek Triremes were named, and naming ideas were not all that dissimilar from modern ship naming: Goddesses, place names, objects, etc.. Names are part of the information contained in the Tabulae Curatorum Navalium in the Epigraphical Museum in Athens.

hi! there are more examples in these posts ~

What is the history of ship naming? What is the first ship we have a name for?

Ships?

Did Zheng He's ships, or pre-modern Chinese ships in general, have names? What sorts of names would they have had?

The earliest known reference to a ship bearing a name comes from records of boat building under the Egyptian Pharoah Sneferu in the 27th c. BC.

Here a recorded vessel of 100 cubits volume and made of Cedar Wood is named as 'praise of the two lands' - a reference to the unification of upper and lower Egypt.

They were! One of the most important documents in the field of Indo-Roman trade which i specialize in is the so-called "Muziris Papyrus". This document gives the name of a particular ship that traveled between Egypt and India as the Hermapollon.