Its called a keiki, and it is indeed a new plant. It can be likened to the baby plants that sprout from spider plant stems. Eventually, probably early next spring, it will have sufficient enough roots you will be able to remove it from the mother plant and pot it on its own. Look under the FAQ's at the very first and 2nd question. They can answer some of your questions.

Valieta, Let me throw my .02 cents worth in here. I grew Den. aggregatum for a number of years. I bloomed mine in South Carolina, Kansas, Florida, and Virginia. The plant comes from around the northern part of India, and ranges from the high altitudes to down in fairly low altitudes. This means that some of them get cool dry periods in the winter, and some get less. the altitude that your plant actually came from may affect its blooming, but then you may have one from low altitudes, and it'll be easy. I had a small greenhouse, so all my plants pretty much lived under the same conditions. my aggregatum may have bloomed out of season a few times...Its been a very long time ago...but really, I did not care because it was beautiful when it did and that was what mattered. I would grow it like a Cattleya, then in the fall/winter shelter it from water as much as possible. The pseudobulbs will shrivel a bit, but expect that. keep the plant out of the sunlight and as cool at night as possible, and hope for the best. One trick that works for some cymbidium growers who live where their plants can't get cool nights to bloom is to put a tray of ice in the pot each night for a few weeks in the fall. That may or may not work for you, because you are in effect watering the plant with ice. You might try a season or two without the ice, and if the plant refuses to bloom, try one season with Ice and see. read up and get familiar with the seasonal weather the plant experiences in its growing area, and do your best to match that where you are. Sometimes its a snap to get plants to bloom in different climates than they are accustomed to, and sometimes its just impossible. Either way, its fun trying. Bill

I also think re-potting them separately would be a good idea. If it were me, I'd use a knife and nick or scrape most of the stems near the bottom. I might even apply some rooting hormone powder to the place I scraped/nicked. Then, I'd bury it deeper, with potting mix covering the scraped/nicked areas on the stems. Give it a couple months, and you could carefully dig things up. If the branches have rooted, you can cut them away from the main plant and have more plants that way. Also, rosemary and sage need really good drainage, and really don't need as much organic material and fertilizer. I add sand or perlite to 'potting mix' for rosemary and sage, about two parts potting mix to one part sand and/or perlite. You can also use commercial "cactus potting mix" if you don't want to mix your own.

There are several different types of dends and each requires slightly different care. My advice would be to go to the Orchid forum in gardenweb - these folks are great at giving advice. I have a decent collection of orchids and learned a lot from them. Be sure to post photos.