while renaming administrator

Don't forget the name :-)
Take care of programs/services using administrator name & PW, like backup softwares or SQL database.

I will not totally rename it you can disable the administrator and create an account and give this admin rights doing it this way you know if anything happens you still have the administrator username in there. and yes do not forget the new user that has admin rights.

Just rename it, it'll keep all it's rights and attributes.

When you rename an account, the SID for the account is NOT changed, and it is the SID that is actually used for everything. So, you can change the Admin account to whatever you feel like, and eventhough it might already be used to run a few Services, Scheduled Jobs, and have specific NTFS security permissions to some files/folders, all "should" go well. The SID is the same, and that is what really matters.
But does this mean that you will experience absolutely no problems? Not necessarily. There are references in Technet about how changing a username has broken things. Just be careful before you do this. I agree with the suggestions that you do an audit first of everything that is using the Admin account. For NTFS permissions, don't worryabout those. I've changed the admin account after giving it permissions on files/folders with no problems. You just need to check the other stuff, just to be safe.

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