I would like to find out what the name of this rose is.
Can You Name This Rose
Here is a link you can go to and enter in known information about the rose, such as color and do a search for the rosebush. Hopefully you will find a matching photo of her here: http://www.helpmefind.com/rose/plants.php With the unique bloom form she has a photo at this great site should get you her name.
It looks like a miniature rose(s) planted in a way too small container. I would transplant it as soon as possible to a larger pot with drainage holes in it. It is truly hard to say which red mini rose this might be but it could be one named Merlot or perhaps one named Red Scentsation.