What I want to do is go to those two countries for a week each. Basically the order doesn't matter much for me. But I must depart from Japan and come back. 

I was wondering if there was someone experienced in this. For example I would think that Japan - Mexico - Venezuela is cheaper since I would go through the United States. But maybe I am wrong, maybe it depends on the season for each country?


Question: Why didn't Palpatine publicly change his name once he became Emperor?
Answer: Only a few knew that Darth Vader was in fact Anakin Skywalker, and those few had no reason to publicize that fact.  Prior to the duel on Mustafar and Padme's death, Anakin may have considered his Sith name to be a working title (had Padme lived, he likely would have still let her call him "Ani" in private), but after his own near-death, disfigurement, confinement to the breath suit, but, worst of all, the belief that he'd murdered his "Angel" and their unborn child, all memory of his life up to that was sheer agony.  Hence why Vader was angry with his own son for being reminded of the family name.  Vader, though to the rest of the Galaxy a powerful figure, second only to the Emperor himself, was behind the mask a sad, lonely, grieving man, in physical and emotional anguish.
To most, Palpatine's Sith abilities were unknown.  They saw him as the man whose leadership had led the Republic through the Clone wars and who raised the Empire out of its ashes (never mind that Darth Sidious himself lit the fire!).  There was EVERY reason to publicly always be Palpatine.