An Ancestor Named Kagome

Inuyasha and his gang take on the task of purifying a cursed sword brought to them by Akitoki Hojo, ancestor to the Hojo in Kagome's time. Back in present day Japan, Kagome finds out that Hojo has ancestor named Kagome, who married Akitoki! What does this mean for Kagome? Does she stay in the feudal era and marry Akitoki, or is it mere coincidence?