There is no email address with just 'icloud' or 'me'.
firstname.lastname@example.org, email@example.com and firstname.lastname@example.org are all the same address (where 'something' is the same throughout of course). If you create an alias on the account it would be email@example.com but would still deliver into the same inbox.
However you can use Rules on the iCloud website to move incoming emails to different versions of the address into separate folders which you would create, so that you could keep them separate. To create a Rule, go to the Mail page at icloud.com and click the cogwheel icon at bottom left: choose 'Rules'.