I think the best possible answer could be
" "?
Or more commonly known as
SilenceSilenceSilenceSilenceSilenceSilenceSilence.......
(I know, I'm pathetic :P)
My name cannot be spelled
While you can write many onomatopoeias down, you can't write silence down, as shown above
It can't be heard or seen
You can't hear or see silence, it is simply the absence of noise
It doesn't make sense but can be understood
It's the absence of noise
It is a common name, yet most have never heard it
It is very difficult to hear silence, because there is usually some sort of noise. It is a common name (often said by teachers or librarians)
It is the most beautiful name, but most hate it
Most hate it because it means they can't speak
What is my name?
It might be silence
