You 're no need to worry about the pregnancy problem.Normally,woman have left and right side tube.Even one tube is cut ,the other side of tubing and the ovary also can be run normally(such as,produce hormones and produce eggs).
Sometimes, if the ovarian cyst too large or have adhesion of the tube and ovary,the doctor may need to cut the tube and ovary.
I also have only 1 ovary and I have 2 girls after the operation. Don't Worry. Mine was a big one and so the whole ovary had to be removed too.
I also have my period every month. So I think I shall 早停經 because instead of having eggs from left and right ovary in alternate month, I have my eggs all from the same ovary every month. I heard that people with one ovary will grow old a bit faster too. I have other 2 friends that have 1 ovary removed too. Very common. One has 2 girls, one has 1 girl.
It won't 影響生育 provided that your other ovary and tube are normal.