To the best of my knowledge, the answer to this question is simply "no." I can't find any source that suggests this. The over-the-top otherness of the supposed custom makes me suspect that if this was actually written down in any ancient source, it was probably Plutarch, whose every claim about Sparta must be taken with a large grain of salt. Plutarch wrote in the time of the Roman Empire, when the heyday of Sparta was 600 years in the past; his account is full of legends and tall tales about the supposed Spartan Way that do not appear in any earlier work.

The traditions we have about Sparta rather suggest that they taught young men to face danger without flinching, standing their ground even when the enemy was close enough to smell their breath. Consider this fragment of a song by the 7th century Spartan poet Tyrtaios:

Abide then, O young men, shoulder to shoulder and fight;
begin not foul flight nor yet be afraid, 
but make the heart in your breasts both great and stout, 
and never shrink when you fight the foe.

Or this one:

Let each man close with the foe, 
and with his own long spear, 
or else with his sword, 
wound and take an enemy,
and setting foot beside foot, 
resting shield against shield, 
crest beside crest, helm beside helm, 
fight his man breast to breast 
with sword or long spear in hand.

Or this description of the Spartans, which Herodotos (7.104.4) puts into the mouth of the exiled Spartan king Demaratos, explaining to Xerxes what sort of men he's up against:

They are free, yet not wholly free: their master is the law, whom they fear much more than your men fear you. They do whatever it bids; and its bidding is always the same, that they must never flee from the battle before any number of men, but must hold their ground and conquer or die.

These were the ideals that young Spartan citizens were raised to aspire to. In reality, of course, they fell far short of them, or else Tyrtaios' encouraging songs would not have been necessary in the first place - but at least it shows how they liked to see themselves. You'll note that this idealised image of battlefield behaviour does not include contempt for the enemy. The enemy is not stripped of his humanity or even mocked. Rather, Spartans were expected to act courageously despite the acknowledged terrifying number and proximity of the enemy.

They did, however, work hard to create an image of themselves as nameless and faceless. The Spartiates, or full Spartan citizens, referred to themselves as "Equals" (homoioi), and they increasingly tried to express this imagined socio-economic egalitarianism in the way they looked and acted. All Spartans wore their hair long and carefully groomed themselves to look taller and more imposing. From the late 5th century BC onward, they seem to have worn uniform red tunics or cloaks in battle - a color that looked fierce and manly, and that hid bloodstains, making the Spartans appear invulnerable. Their shields were coated in polished bronze and adorned with the lambda signifying Lakedaimon, their home region. The result of all this uniform display was that the Classical Spartan phalanx looked like a single mass, "all bronze, all scarlet", rolling across the battlefield like an unstoppable force. Few had the nerve to stand up to them. Finally, when a Spartan died, in contrast with general Greek custom, he was not allowed a private grave monument with his name on it, unless he fell in battle - in which case he was allowed no more than a simple stone with his name and the words "in war".

With that in mind, it seems more likely that the Spartans would have done the opposite of what you've read. Rather than portraying their enemies as nameless and faceless, they would have drawn a contrast between their own disciplined, uniform, collective appearance and the clumsiness of their disorganised enemies. The more individual the enemy was, the less like a Spartan he was, and therefore the more worthy of contempt.