Known. A Roman floor mosaic shows a cat and a dog, each with a name in Greek letters.
The floor is at Adramytteion, in Turkey. It is 1,800 years old. It measures about 5 metres by 3.6 metres and has 15 framed panels. It lay in the north hall of a villa, where guests would see it. A pale cat sits beside letters read as Emerald. A running dog appears with letters read as Ocean. Fish, birds, and other figures fill the rest of the floor.
The page says it is not yet proved that these pictures are portraits of real pets.
https://www.ancient-origins.net/news-history-archaeology/roman-pet-mosaic-00103157