Re: "Sometimes one name works but I can't figure out what to do with that because the other three are for the opposite parent, etc." Those surnames in the list are just any direct-line surnames that occur in both your tree and the match's tree.
They are not inclusive. I have a great match, an exact match through an ancestry provided overlapping surname in one tree. Perfect. In another tree, I have that person's parents and yet these people were not included in the ancestry provided overlapping surname and a completely different surname was given (which I couldn't make work).