Also how well known were family members to each other. Obviously outside of the immediate family i'n guessing after generations Kings would have hundreds of cousins from various royal uncles and aunts so how would they keep track of everyone? Would their be royal family gatherings with everyone in attendance?
First of all, see the FAQ for questions about proof of identity.
That said, the answer is generally speaking no. While it is true that extneded royal or noble families could be very large, if someone were to show up and claim to be person X of some standing he would be expected to carry a letter of introduction of some sort. Basically, a letter from signed and sealed by someone well known at the destination verifying that the the bearer really is person X. If he did not, he would likely come under very close scrutiny.