Or we could follow Shakespeare's lead and not worry about spelling too much. Plenty of named also get anglicized into slightly different or multiple spellings. Are those Chinese people called Wang or Wong?
Not just his own name, nobody at that time could spell English consistently. Which might have had something to do with not even being able to read or write.
People's names are fundamentally oral and spelling is just an encoding to communicate them in writing. Being worried about spelling correctness it like being worried about the choice of binary encoding of the spelling. My name is only correctly encoded in binary as ASCII, not some bastardized similar-looking unicode codepoints, and certainly not that archaic IBM encoding! Future generations had better respect my preference! /s
It's the same character in both dialects. I don't think a particular romanization counts as somebody's language when plenty of native speakers can't even read or write it. If you want to respect spellings, we should write all Chinese names in Chinese characters, but we don't because we don't respect them enough to actually bother with effort.