OK I'm going to outline a plan for naming our units. I hope it helps.
Firstly: Let's assume that a) we are going to follow Rik's advise and name our units with their 'type' (eg. Warrior or Knight or Bomber) and b) That we like the idea of using the Gods as a basis for naming our units.
Secondly: Here is a link to a list of the Greek Pantheon of Gods
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So!....
I suggest the following system gets used for naming our units. It can be consistent, practical and colourful.
Each unit has 3 names (and these can be put in any order).
a) God Head of Unit Class / Division
b) The actual unit name (eg. warrior)
c) A Number or specific name for identifying the individual.
So we will have units with names like:
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"Zeus Nuke 1"
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"Athens 1 Poseidon Frigate" (cos it was the first built in Athens)
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"Assyrian Ares Warrior" (cos it defeated Assyrian Barbs)
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"Pan's Persepolis Sacking Cavalry" (cos it was part of the successful assault on the Persian Capital)
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Explanations:
a) God name. We can assign a Greek God to a particular class of unit, may I boldly suggest:
CLASS/DIVISION..................................................GOD HEAD
Infantry Defense (Spear > Infantry)............................
Hermes
(cairn) Son of Zeus, and a Deity of many functions and attributes. He is best known as the Messenger and Herald of the Gods, but he is also a fertility God, a Lord of fortune and fate, and a patron of both merchants and thieves. As Herald he combines patronage of Music and Eloquence, and as Divine Messenger he controls dreams and omens. Quite expectedly, he is also a Protector of travelers. His name refers to boundary stones and landmarks.
Infantry Attack (Warrior, Archer > Marines)..................
Ares
(warrior) Son of Zeus, and God of warfare and battle. His was an unsavoury repute among the Hellenes; he represented to them the savagery and chaos of battle. His cult was most common among northerners; Epirotes, Makedonians, and Thessalians; and in the south among Spartans.
Mounted (Horseman > Cavalry)...................................
Pan
(pasturer) Goat-footed and horned God of field, grove, and wooded glen. The son of Hermes, he was a shepherds Divinity, concerned with fertility, the wildwood, and solitary pipe-music. He had a somewhat disreputable image in the Classic world on account of his trenchent lustfulness, but was very popular as an artistic theme on amphorae and wall decor.
Mechanised (Mech Inf, Tanks etc)..............................
Nemesis
(due enactment) Child of Nyx, Goddess of divine vengeance, and implacable retribution. She is usually imaged bearing a scourge and a wheel.
Artillery (Catapults > Artillery)....................................
Herakles
(glorious protector) Son of Zeus and a mortal, he has a very rich and complex mythology associated with him. As a mortal, his travels and adventures are legendary, and he has become known as the quintessential Hero. His journeys and labors can be seen as an initiatory sequence, in which his Earthly dross is gradually purged from him. His demise is the final act of this process, and on his funeral pyre his Spirit is liberated, and ascends to Olympus where he is admitted to the company of the Gods. He was a popular cult figure throughout the Classic world, and his tale still holds attention today. His favored weapons were the club or maul, and the bow.
Naval Transporter....................................................
Proteus
A Divinity of the sea, the herder of the sea's "flocks" (seals and suchlike). Imaged as an grumpy old man, he was a wisdom-master, and knows all things, past, present, and future. He will not divulge his knowledge unless, catching him unawares, one can bind him sufficient to keep him, even though he can change his shape at will. Caught, he will answer one question, then escape into the sea.
Naval Attack (Frigates, Battleships etc).......................
Poseidon
Son of Kronos and Rhea, principle God of the Sea, in concert with many other spirits, godlings and Deities of that Realm. He also had patronage over horses, and in fact was said to have created them.
Air Force................................................................
Persephone
Daughter of Demeter, beloved of Hades. He kidnapped her and took her to his Under-Earth Realm, where she pined for the sun and the sky. Her mother searched over all the land for her and, not finding her, withdrew Her Attribute from the land, causing barreness and destruction. Zeus intervened and it was dicovered where Persephone had been taken. She could not be released, however, because she had tasted some nourishment, a single pomagranate seed. Nevertheless an arrangement was worked out whereby She might visit Upper-Earth for half a year. Her movements henceforth herald the coming of Summer and Winter.
Nukes..........................................................................
Zeus
The thunderbolts duh!
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b) The unit name is the name of the unit. Get it. Warriors are 'warrior' etc.
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c) Individual Identifier Name: This can be a number, a memorial of a battle, where it was built, an area we have named and associate with it etc.
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What a waste of a lunch break
... I'd have more fun naming my own city when it comes to my turn ... not wandering through the pages of a greek history text ... 
them.
