Living in working in Japan and some names pop up quite frequently. Right now I'm in Hiroshima where the Mori were famous.
If I meet someone with that last name, or any other power feudal family, is there a high chance that someone today with their last name is a descendant?
It's unlikely that the names of these people would mean them to be direct descendants of various shoguns/daimyos. Mori, for instance, is written two ways in Japanese, 毛利 or Mouri (ou is long ohh sound), and 森 or Mori ( short oh sound ) Not only this, but the commonality of Japanese names in general and the homophonic names with different meanings makes it very unlikely.