Most Ancient Greek names have a literal meaning in Ancient Greek; they are composed of existing words, derivatives of words, or of other names. The common suffixes are simply popular elements in these names.

The ending "-kles" is the common name variant of kleos, meaning "fame" or "glory"; hence Herakles means "fame of Hera" (a rather sarcastic name given his parentage). Themistokles son of Neokles is "glorious privilege, son of new glory". Sophokles is "glory of wisdom" or "wise fame". The name Patroklos ("fame of the father") is one of the rare examples where kleos is turned into the suffix "-klos" rather than "-kles". Its female equivalent, Kleopatra, retains both vowels.

Achilleus is not an example of the kleos ending; the meaning of his name is actually obscure, and possibly predates the Greek language.

Other common suffixes are "-krates" meaning "power" (Sokrates, Hippokrates); "-andros" meaning "man/of men" (Lysander, Periander, Anaximander, Alexander); "-machos" meaning "battle" (Kallimachos, Lysimachos, Andromache); "-stratos" meaning "army" (Peisistratos, Philostratos, Archestrate); "-archos" meaning "leader" (Hipparchos, Aristarchos); "-sthenes" meaning "might" (Demosthenes, Eratosthenes) and so on. They all have a direct meaning, usually a reference to something admirable or aspirational. Often the reference is to old Homeric values (bia "strength", kleos "glory", timê "honour"). I wrote more about Greek naming conventions here.