I live on the Miura peninsular not too far from William Adams fiefdom. It’s possible to walk up the hill from Anjinzuka Station (The navigator’s hill) and see his and his wife’s grave.
Was there really a legitimate legal issue needed to be accounted for at the time, across these borders? Additionally, ostensibly to Adams, it would have been something he would have to answer to his creator for moreso than the crown or Shogun, if he was a true believer anyway.
Polygamy (as in being married to more than one person) isn't and wasn't legal in Japan. I don't see how it would in any way be feasible or acceptable to take a new wife in Japan of all places, where honor and family are such important aspects of their culture, while already married.
I understand OP's question to be more practical than honour and family - literally as "Would the Japanese recognise a marriage performed in England?".
Civil registration started in England only in 1837. Modern koseki system in Japan started in 1872, but different systems of civil registration existed way before that, including one created under the shogunate (though many years after Adams's passing).
And indeed, they couldn't possibly careless about his married status regarding him marrying a Japanese woman. His declaration of death was so that he would be free to serve the shogunate freely, without the obligation of return to his family in England.
> Additionally, ostensibly to Adams, it would have been something he would have to answer to his creator for moreso than the crown or Shogun, if he was a true believer anyway.
I mean, bear in mind that about 30 years before Adams was born, Henry VIII had broken with Rome so that he could get a divorce. Religious views on the sanctity of marriage in England were, ah, evolving rapidly at this point.
I mean, Henry certainly _claimed_ that it was an annulment, but it was self-granted, on a basis seemingly made up for the occasion, so realistically considering it to be an annulment was a _bit_ of a stretch.
(Not that this was exactly unprecedented; the whole thing kind of came to a head because the Pope wouldn't grant a spurious annulment to cover a divorce to Henry, but various Popes had certainly granted dodgy annulments to various monarchs _before_.)