Honestly, I really am trying, but as far as I can see you are using the word "named" in a sense that allows most numbers to be called "0". I really can't see how your words make sense given any other definition. Is that correct?
That is essentially correct, and we actually do call many different numbers "0" in different contexts, but it's not necessary for any two numbers to share a name this way. You can give them all unique finite names with an infinitely large alphabet if you prefer.
You might consider that in the existing Chinese writing system, 口 and 囗 are distinct symbols.
