No,, if you rename an existing account, it is tied to it's original name underneath it all.
If you want to fully change the name completely, you have to create an account with that name.
Incidentally, I would have just left the main admin account as admin and just created a new Standard user account. There is no reason to create a new admin account and then change the old admin to standard.
To me, that is creating more work than needed.
I missed something,,ooppss.
More Info - ....
I could be wrong, but I don't think this is the same as days of old NT, where you wanted to create a new admin account and disable the original Built-in admin account due to the SID S-1-5-21.
It used to be defined as good security practice to do this as the built-in admin account was a well know SID that could be used to hack the system
Something I might look into. If that is the case, then this is how it should be done....
Install and setup windows
Create new accounts (Standard User and Admin accounts, at least one each)
Then go in and don't delete but disable the original admin account
This will change the SID, so that the original S-1-5-21 (Admin account) is not the same as the Built-In SID
This could be an old way of thinking though.