Is Erza's samurai costume considered an armor? That famous costume where her hair is tied in a very long huge pony tail and she has only bandages on her torso and this baggy red hakama pants with a katana.

Is that an armor? If so, what's the name?
There really is no name for the armor, some people call it the Japanese Cloth armor but the fact is that it is not really armor. It is a completely offensive requip in which she puts all of her power into her sword for attacks. On the wiki page for her battle against Azuma it states:


  Erza decides that in order to defeat him, she has to collect all of her Magic into a single offensive attack without wasting any on defensive power. She requips into her Japanese-like clothes, previously used in her battle against Ikaruga in, stating that she has no need for armor and only her sword. 


On her wiki page you can see that the requip in question is not listed. 
For a complete listing of her armors you can find that here: Armors