Yes, if Jutaro knows where his ancestors are buried, he might find his family's kamon on their gravestones. (Or, if really lucky, we might be able to find them using google maps, but its a bit unlikely). Other places he might find it are on family heirlooms like kimono.
But if somebody says, "My last name is Tanaka, please tell me what m kamon is", it would be impossible. There are Tanakas found all across Japan, and there are many, many kamon associated with the name Tanaka (or Watanabe, or Sato, or Saito, or most any Japanese name).