I registered my eos erc20 token before the snapshot happen and kept it in my ether wallet. I was given an account name, my public key and private key. If I create new account name on Infinito Walle...

Not linked in a traditional sense. However, you can Import your existing EOS private key. Then all of the EOS account names associated with that private key will be loaded, and you can enjoy the rich feature that Infinito Wallet offers for EOS blockchain like making transactions, Stake / Unstake your CPU / NET bandwitdh, Purchase / Sell RAM, etc. Please keep this imported EOS Private Key safe. It cannot be restored using your wallet passphrase and therefore, must be managed separately from your wallet passphrase