You can actually do this, although I can't imagine any reason why you would want to. You can create a new user with the same user ID (UID) as root. Note that this isn't actually a "new" user, it is just a different user name for the same user. However, you will be able to log in using this name instead of root.
First, create a new user and set their UID to 0, the UID of the root account:
useradd -d /fool -g root -m -N -o -u 0 -s /bin/bash fool
The options used are:
-d /fool : set this user's $HOME to /fool.
-g root : set this user's default group to root.
-m: create the user's home directory if it does not exist.
-N: do not create a group with the same name as the user, just add the user to the group specified by -g.
-o: allow the creation of a user with the same UID as another, existing user.
-u 0: set this user's UID to 0 (same as root).
-s /bin/bash: set the user's default login shell to bash.
fool: the user name will be fool.
After running this command, you will be able to log in as fool:
terdon@ub20:~$ sudo -iu fool
root@ub20:~# whoami
root
root@ub20:~# cd
root@ub20:~# pwd
/fool
As you can see, I have logged in as fool, but whoami (which is based on the UID) sees me as root, while cd will take me to /fool. I have all the rights of the root user, because I am the root user, but my user name and home directories are different. You can now proceed to allow root access over ssh (at your own peril) and log in as fool instead of root. This is all cosmetic, you're still really logging in as root, but that's what you seem to want.