Every fridge makes sound, there are only silent ones. Check out lots of online reviews (make sure the websites are neutral).
I lived in a single room studio apartment for five years and I got used to my fridge eventually, it was quite big and had a low hum, so I have no idea what type of sound the smaller models make.

Thanks. I will continue my search.

Depending on your budget, you might want to consider having a good contractor put the compressor in another area, so you don't have to deal with the noise. There was a Houzz Ideabook a year or so back where the home-owners had this done, and we plan to do it in our new house, I hope.

Little fridges are often VERY noisy, as they work hard.

We have a haier welbilt frigerator. Outside dimensions is 19" x 19" I have to put my head close to door to hear the compressor humming sound.

Our small subzero fridge doesn't make noise, and keeps things really cold which I love!