Mad is up to you.
But John and Joao are definitely not the same name. If someone asks you "is your name John or Joao?", even in Brazil there's only one right answer. At best you can say "both names can trace their origin to the same root name", but they are not the same name.
The Mexican guy's name or your anecdote is named Joe (but pronounced like he or his parents wanted it). There are no two ways about it.
In Argentina and Uruguay some people are called "Jonathan", only pronounced "Shonatan" (or in some Spanish pronunciations, "Yonatan"). That's the way it is.
Finally, phonetically spelling the name and surname of a known celebrity, as in Wozniak's case, just seems silly to me.
Is the president of the US You Baiden? That's a phonetic spelling in Spanish, after all! (Silly, right?).