Adding to the complication is the fact it is also a man's name.
Even in cases where both first and last names are known and there is an old address or at least some general idea where they lived it is practically impossible to track down most people here. Public records aren't accessible to third parties and in almost all cases it is impossible to look up phone numbers and addresses online. If the woman has since married and you don't know her married name, it is pretty much a lost cause.
Not to rain on your parade, but if this woman meant so little to you at the time that you couldn't even be bothered to remember her last name or hang onto any communications from her, then it looks like you're just trying to get in touch with somebody who was nothing more to you than a hot piece of tail and I doubt any efforts on your part would result in a nationwide viral manhunt or that she would be thrilled at being found under such circumstances even if it did.
Look, I was also military in Japan around that time. Guys our age still had the WWII and Occupation Era veterans around. You never ran into those guys? The ones who in the 1980s told you they were in Japan in the 1950s and asked you "Do you know Sachiko?" And did you not think "Does this guy think there's only one Sachiko in the whole damned country!?!?!" Well, it is deja vu all over again but you have graduated to the starring role.