According to the book known as "The Acts of the Apostles" St. Paul famously noted that the Athenians had an altar dedicated to "the unknown god" and expounded on it to their edification, using it as an example of pagan superstition or pagan piety, depending on just what translation is being read. I personally find the notion more Roman than Greek. The thorough, prudent Romans it seems to me would be more likely to see to it that an unknown, that is to say un-named, god be worshipped--just in case that worship should be appropriate or required for one reason or another.
The Roman religion as we know it, before it became Greek, was most practical, though the gods or spirits they were devoted to were often ill-defined. This has sometimes been claimed to indicate that they lacked imagination, unlike the Greeks, whose gods they would assimilate. The gods of the popular religion of ancient Greece certainly were fanciful, but if they're considered indicative of imagination I think that imagination is not particularly imaginative, as it consisted of extrapolation from human characteristics well known to any of us.
Though the gods were undefined in ancient Roman religion the means by which they were to be worshipped were detailed, even rigorous, and the rituals were to be carefully performed, without error. This precision was owed to the divine. If there was error, then they had no effect and were to be repeated. The Emperor Julian is said to have repeated a particular rite when interrupted, and it is doubtful that at the time he did so the rite in question involved one of the ancient Roman divinities, as it would have taken place in the 4th century CE. So the need to perform the rite properly seems to have survived if not the god or spirit itself.
It seems that the more a conception of God is such that the characteristics ascribed to God are unknown, the more reasonable that conception becomes. To the extent that God's characteristics are well known, it seems those characteristics are necessarily shared by humans. For those of us who find it difficult to be impressed by a human-god, or feel that a human-god doesn't quite rise to the level of a God of a vast universe, this is unsatisfying. This I think is why we find that what is called the "God of the philosophers" and the God most referred to by theologians, even Christian theologians, is quite abstract, and may even be said to be unknown, or unknowable, as a result. In any event, a human-god is clearly a god of a kind which is limited, as it is one which is the special concern if not creation of our race on our tiny little planet in our tiny little solar system.
It's interesting that the more abstract our conception of God, the less likely it is that God will be a "jealous" god, or angry god, or demanding god. It's difficult to ascribe to the God of the universe a keen interest in our sex lives, or in the manner in which we dress, or whether we act or do not act in certain ways on certain days. Intolerant gods are little gods. They're not great in any sense.
But little gods may be what we humans need until we have rid ourselves of our overwhelming selfishness. As long as we look upon the universe as ours alone, as long as we think of ourselves as determining the universe, the divine will always be human.