Well, let's face it: if you're looking for a Successful Medieval Militarist, the Mongols are in a class by themselves historically.
However, one or two things about the nomenclature chosen, as others have noticed.
"Horde" is a Turkic word, not Mongol at all. The perfectly Mongolian word that could have been used would be Tuman, which indicated a unit of 10,000 warriors, and so certainly evokes the image of a Horde.
Also, each Tuman had its own standard and title, which would be a nice touch for 'personalizing' your Mongolian units.
As for the Orda or Ordo, It's related to the Turkic word for 'camp' - orda, but in Mongolian it usually means 'palace' - "place of the ruler', which I suppose makes it Special enough to be Emblematic. It is also related to the Turkic word Horde, as in a large group of people, not necessarily warriors, so, again, could be used for a group settled in a city.
Just to note, though, that the traditional Mongolian tent dwelling is the ger, the Mongolian version of the Turkic yurt, and Ger would have been a very 'emblematic' term for a 'semi-settled' nomadic District/Quarter in a city.
Oh well, the real question is how they are going to differentiate the Mongol Faction from the Hun Faction besides, presumably, better Combat Factors for the Mongolian Horde versus the Hunnic Horde. I really hope they have some mechanism that replicates the Mongols' much better integration of other groups into their Empire and so much better stability of their Empire: the Huns were notoriously ripped to pieces by their own subordinates as soon as they faltered, while the various Mongolian and Mongolian Successor Factions lasted centuries.