And here is a screen shot showing an Ancestry hint. Note that his match was a very low probability distant cousin who ended up being much closer than predicted.
I agree that one should click on the surname, and also look for all people of that surname in the list of names in your match's tree, since your connection may be with a sibling who is not a direct ancestor.
One further point, which I have made before, regarding going beyond shared surnames. I have a 95% 4-6 cousin match with a man named Kelly, a surname that is not in my tree, and none of my family's surnames are in his. However he has an ancestor named Driscoll, a common name in my family's home area in Ireland. His Driscoll ancestor's parents were not listed in his tree, however I found them in online Irish records and his mother was my 2xGGM's niece. This made him a 4th cousin once removed, a match which confirmed my ancestor's first name and place of origin.