Make very sure you know which things you can and cannot take. I'm not talking so much about in the hospital (though it never hurts to be alert for medication errors), but you should definitely mention your one-kidney status to your family doc, pharmacist, etc.--and don't be shy to remind them.
A few days after writing the above words, I happened to be at my family doc, who recommended I take aspirin or Ibuprofin for something. [Apart from my general reluctance to take any pain meds,] I reminded him of my donation, and that the "NSAIDS" category of meds is supposed to be forbidden for us one-kidney types. He quickly agreed, and apologized. No harm done.
But, note well: this doc knows me very, very well, and processed much of the mountains of medical tests and paperwork for my donation and post-surgical follow-up. In fact, we usually chat about the donation whenever I'm there. So he really should have remembered But doctors are very busy, and are only human. So, as I've written many times,
you are your own best advocate.
Be well, Snoopy