Be sure and see a Urologist, first and foremost. Then, get him to tell you where on the 'Bosniak Scale' your cyst falls (http://www.kidneycancerknol.com/index.php/Bosniak). I have NUMEROUS renal cysts on my left kidney (too many to count) and they are mostly Cat.2 & 2F. Luckily for me, no cancer detected yet (fingers crossed).
If your Urologist feels your cyst is operable and it's necessary to remove it/them, they'll perform a Cyst-Decortication. They basically shave off the top of the cyst, drain the fluid, and cauterize it. It can be done laparoscopically and doesn't require open-surgery. I had one done recently and was in-patient for 3 days, and most of that was getting a nagging fever down.
Don't sweat the 1-kidney thing. You've been like this your whole life, and if not for the cyst, you may never have known. Now that you know, just try to stay healthy. I cut alcohol out of my intake 100%. Not sure if that's an option for you, but if it is, I strongly suggest you doing the same.
Good luck to you!
Correction to my last post, I just googled it....... there is a name for a single/solitary kidney it's called "renal agenesis"
You have polycystic kidney disease.
As far a no left kidney I'm not sure if there's a name for that condition. I too was born with only one kidney, Dr never did mention a name nor if it's a condition other than "birth defects"