Be sure to post pictures as soon as it blooms, I can't really help by looking at foliage :)

I can't offer an ID, but as for care, keep watering and weeding it, and give it some nice compost/ organic matter/ liquid seaweed and/ or some organic fertilizer for roses. There are lots of types available, but Rose-Tone may be the easiest to find?

Clearly, that's a survivor, but surviving and thriving are not the same things- some nutrient-rich soil will help your 'new' plant do more than just exist...

It looks pretty healthy, maybe just a little undernourished. I agree with vmr423. It just needs some tender loving care.. make sure it is getting plenty of water, especially if you live in a hot dry locations. A good organic rose fertilizer, fish and kelp fertilizer are good organics fertilizers to add with you rose specific fertilizer. It can take a while to bounce back, but with a little care you will be sending us a picture soon. It may need a little pruning which you should probably get some help with the first time. This will help it produce new buds and clear out any diseased canes. We all started with one rose and many of us now have hundreds.. once you get started it is hard to stop. Have fun with it. The nursery people can be very helpful.

Mallory, has your rose bloomed yet? Is it setting buds? If there are no buds yet it could be the root stock coming up from a grafted rose that has died. Several types of root stocks are once a year bloomers on old wood. That means it won't bloom until next year on the canes it grew this year. It would help if you posted your zone too.