I’ve probably engraved a thousand mugs, baby cups, chalices and many other assorted vessels like this. As the others suggested - ask the buyer first.
I did read in an old Engravers journal that the person so honored to have their name engraved on their cup, should display that honor to those who would read the inscription while the owner held and drank from the vessel.
So, interpret that for yourself - I always assumed the honored soul would lift the stem or handle with his right hand?
There are similar discussions in other ancient engraving books that suggest which direction an engraved ring should be worn; I.e., to honor oneself with the image toward wearor or to proudly display outwardly for others to appreciate.