Not really. You're comparing a modern name issue with a different age. A similar thing happened regarding 9/11 and to this day some of the 911 deniers think the hijackers were still alive, when in fact it was just other men with the same names. Not surprising.
But if you are denying the man wrote the plays, then you have to establish who actually did. It had to have been someone within the company or someone extremely familiar with them, because again, without knowing the features and abilities of the company you do not know what they can do on stage. You cannot mail that in from his Lordship's house. Shakespeare's plays also evolved as the company did, such as the comic role changing 'type' when one actor left the company and was replaced.
I think you're tending to prove my point ! Don't fixate on names. They prove nothing.
Shaxper/Shakespeare
Nakamoto/Nakamoto
Atta/Atta
Focus on evidence, the most reliable yardstick.
Where is the evidence Shaxper was Shakespeare?
Nothing, until seven years after Shaxper's death, and then only a cryptic assertion in poetry, accompanied by a bizarre engraving, in the expensive First Folio.
Should we expect some independent evidence? Almost certainly. [116,000 TO 1, statistically, based on contemporary writers' surviving records]
Why are there literally none linking Shaxper to "Shakespeare" in Shaxper's lifetime, when we nevertheless know lots about Shaxper through surviving records?
Answer: Most likely Shaxper wasn't "Shakespeare", no more than "Atta" was Atta or Nakamoto is "Nakamoto".
Who
did write "Shakespeare", if not Shaxper, is harder to prove.
By definition, if the author positively sought anonymity...
"The Treasure of the Sierra Madre" was written by "B. Traven"
Of course, it is no use looking in the phone book for a B. Traven and trying to link that person to the famous book. B. Traven was a pseudonym, the true author still hotly debated.
Traven - whoever he was - said something interesting and profound however.
"The creative person should have no other biography than his works...."