the surname of my matches great grandmother and my great great grandmother are the same.
Do you mean that the mother of your and the match's great-grandmother is the same, but the father is different?
If no paper trial can be found that's the route to take. It will involve going through all the shared matches that appear to be on this line. If there tree is not complete, open up dead-ends and search for them in public trees. There is a [search] button at the top-right of each profile. The line is often continued, or if not, you might be able to find records. It doesn't take a huge amount of time to go through each one.
It's important to make sure that the matches are common matches. Some matches overlap with some and not others, like this:

You can find that some matches' trees might happen to have (supposed) ancestors in, but don't overlap with others that have them. In such cases, there might not be a link.
You could also have matches that indicate shared ancestry with a match, but there are no shared matches between you.