One unusual aspect of this painting is that normally Holbein produced portraits of living subjects and would present them as themselves. In this case he would need to find a model who could play the role of this Greek character. The lady chosen actually appeared again in another Holbein portrait of around the same time, though it didn't alter his general preference for portraying real life subjects.
Perhaps in some cases the artist would be forced to produce portraits of donors in any case, in order to receive their commissioned wage. Perhaps paintings such as this one, therefore, offered something of a break to the artist and a change of direction that renewed his creative mind. He may have felt the same with his most famous painting, Ambassadors, which zoomed out to reveal fuller length figures, along with a much more detailed background.
Artist Holbein places the name of this painting in the bottom row, styling it as if it was part of a frame. This technique was commonly used by Netherlandish painter, Jan van Eyck, who perhaps paid more attention to a painting's frame than any other artist from the Renaissance. He saw it as an extension to the artwork, rather than just a presentational tool.