The Greek names reflect the values and culture of the society on the time of origin. The names relate to their language, religion, and political life. The Greek civilization is one of the oldest civilizations. So, they have long history and rich culture. Their history spans as far as 13th century BC. Their names appeared in ancient tombstone, vases, papyri, inscriptions, coins, gems, manuscripts, seals, and stamps.
In the past, their main purpose to name is to identify. The name validates your language, religion, ethnic origin, civic subdivision, and political life. Their name may include the given name, parents name, ethnic origin, and civic subdivision.
During the 13th century BC, their names are only one given name. In literature, ancient Greeks are usually identified by only one name -- whether male (e.g., Socrates) or female (e.g., Thais). This is absolutely true for female or male baby names. The given name is enough to identify themselves. Perhaps, the population is so less at the time. For example, Socrates, Alexander, Thais, and Homer are example of given names. Traditionally, the first born are given the name of the paternal grandfather. And for the second born, they are given the name of the paternal grandmother.
Then, the use of parents name comes into play. The parents name tells the family where you belong. The parents name improves the ability to legitimately identify a person. For example, Socrates son of Homer, or Alexander son of Adelphos legitimately identifies the person and family. In Athens, it became mandatory in 403/2 B.C. to use the demotic (the name of their deme) in addition to the regular name on official records.
It was also common to use an adjective to show place of origin when abroad. As they started to move from one place to another, the Greeks saw the need to tell the origin. A city may be divided into organization. In the name, the Greeks will include the organization. In English we see this in such names as Solon of Athens or Aspasia of Miletus. For example, Alexander son of Adelphos, Athens or Socrates son of Homer, of the deme Athens tells the family and organization of origin of an individual.
The name could be simple or compound. The simple names are made of a noun or adjective. For example, Cressida, Ophira, and Titian are baby names meaning gold. Another example, Zoilo, Zosima, Zosimo, and Zotico are baby names meaning lively.
The compound baby names are combination of nouns or adjectives. For example, Niko-Lysandra means victorious liberator. Another example, Nicodermus means victory of the people. It is a combination of Nicole and demes. Nicole means victory, while demes mean organization or people.