What I read in the whitepaper is this statement:
PLEASE NOTE: CRYPTOGRAPHIC TOKENS REFERRED TO IN THIS WHITE PAPER REFER TO CRYPTOGRAPHIC TOKENS ON A LAUNCHED BLOCKCHAIN THAT ADOPTS THE EOS.IO SOFTWARE. THEY DO NOT REFER TO THE ERC-20 COMPATIBLE TOKENS BEING DISTRIBUTED ON THE ETHEREUM BLOCKCHAIN IN CONNECTION WITH THE EOS TOKEN DISTRIBUTION.

What I understand is that any new blockchain using the EOS,io software will be equipped with a new token, with a name of choice. This new token will be key to the functioning of this new blockchain. The EOS token we bought a few weeks ago, has no relation to any blockchain using the EOS.io software, nor is it intended to be so. It is a coin without use or function.