It's probably Miscanthus which is considered an ornamental grass.

It's a cool season grass, Susan, best moved when it's putting on growth in spring so they say. I suspect it's either already in or approaching dormancy and it won't get busy putting out roots if moved now. I've never moved an OG in fall so I can't say one way or the other if it'll survive, but if you really don't want to lose it, then I'd wait. On the other hand, if you can get the entire root ball with lots of soil so that it doesn't disturb the root system at all, then perhaps it'll be okay to move, but maybe wait until spring to divide it.

Thanks for the info about planting the warm season grasses. As far as the half completed lasagna bed, I pulled back some today and saw Worms!! This is good. So now I feel a little better about pulling this back, amending planting holes and then puting the lasagna compost back on the ground. It should continue the positive improvements I just saw. The NC area I live in, called the RTP area, is notorious for clay soil and land that does not perk. We live in a geological formation that has soil created from weathered sandstone and shale. The big "no no" around here is adding sand. It will make concrete here. They do say you can use washed "sharp sand". I am going to amend my planting holes with a lot of organic material, dig extra wide holes and elevate the plantings. I do not think I will be able to raise the entire area. I will incorporate some of the lasagna bed compost. I am also researching gravel to add to the planting holes. I have read some about 1/4 -10 gravel. This is a mix of 1/4 inch and .196 inch washed gravel with no fines. The fines being the very small particles that help make concrete with the clay soil. Seems like this is being used a lot in the Pacific Northeast. The gravel folks around here have never heard of this but they have something very similar called 78 gravel. I read an article by "Wind Dancer Garden" where they indicated they use this in all of their gardens to help soil drainage, I read on another web site where they even use this to plant lawn grass. My main problem now is getting this clay soil dry enough to work. Got all of my grasses and I am ready to plant! One other thing, the m. Graziella and m. Silberfeder I bought from Sooner Nursey seemed to have come in good shape. Nice size plants for 1 gallon containers. I have never purchased mail order plants before. I may have got lucky in ordering early and getting leftovers from last year before they got their regular stock in for the year. These may be larger plants than their normal 1 gallon plants.

The only ferts my grasses get is an occasional bit of compost tea, very dilute. Apart from that, they get nutrients from decomposing mulch and that's it. Ornamental grasses really don't benefit from overly fertile soil, and can get too floppy if there's too much nutrient. I remember reading, on this forum, someone's experience with lawn ferts and A. donax, and I believe it was a positive one. I've never grown it, so I can't speak to it's need for ferts. I wouldn't put any Weed-n-Feed type stuff anywhere near any ornamental grasses, but I don't use any of it anyway. I'm trying to get rid of lawn, not encourage it.