Yes, when you pull up a match page, the surname matching is done right then. So, any changes you make will be reflected the next time someone pulls up your page.
I played with this a bit when I had a match who matched me two ways. I changed the name of the common ancestor in our Shared Ancestor Hint to "Zzzzzzz" to see if the other line would be displayed as the Shared Ancestor instead. All I had to do was hit "Reload" and the new hint was there, and the surname "Zzzzzzz" was now in my surname list, lol. :)
(Such a pity that Ancesty can't show more than one hint.)