Many painters are signing their monograms or names on painting. What is it representing? Simply it can be mean that they are proving the artwork value with their name.
Euthykartides the Naxian dedicated me, having made [me]
The only things we know about Euthykartides are what the toes, the base, and its inscription – probably the earliest Greek sculptor’s signature, certainly the earliest complete one – tell us. The man was from Naxos; he dedicated (the word is anetheke∗) a statue that he carved in a sanctuary that (largely because of Naxian investment) was fast becoming one of the most important in Greece.
What is the meaning of signature? The earliest Greek signature was not on present evidence an “individual artistic genius” who used his sculptures self-consciously to “express himself” or his “inner vision” or his “originality.” And his statue was probably completely conventional, even if the convention itself was in its infancy: (1)
The first signature could for the dedication his name to the god or promoting his name to buyers, or even he was proud of his skill. However, regardless of his purpose, his name replaced himself to the carved another sculpture figure. Follow the passed time, we cannot guess who it is - at least we know he is from Naxos - cannot guess how he looked like, but the image of carved shadow replaced his own image as Euthykartides.
(1) Hurwit, J. (n.d.). Artists and signatures in ancient Greece. 1st ed. New York: Cambridge University Press.