Hi there! I've been driving my 2010 RX 450h for around 8 years, and while I was changing a tire yesterday, I discovered some problems with the rear suspension. I'm not sure what the specific part is called, so could someone guide me on how to replace it?

 

Welcone to CL. If you did not know that that item is the spring, and that the upper spring mount appears damaged, then you should not attempt any repairs or further inspection of it yourself.
You probably do not have the tools or high level skills to deal with replacing a spring or diagnosing exactly what is wrong. Your single photo is insufficient for diagnosis. You need a shop to determine why the upper spring mount appears to be out of place. I would find a local independent shops that works on Toyotas. Try Google or Yelp for reviews. I would not take a 14 year old car to a dealer. They will make up some very expensive repair to scare you into buying a new car.

Springs can be quite dangerous due to the pent up energy. When parts are separated, you could be injured or worse. Do not try to take it apart yourself.
Are you in the rust belt? Has it been in an accident? Was it a simple flat tire, or did you hit something on the road that may have caused this damage?