I assume you're talking about the Administrator account (possibly the only one on the machine)..."root" is something very different and something most users should never need to see or deal with.
In Tiger, you can change the name on a user account, but Apple frowns upon it, as it may cause some issues.
Here is their guide to doing so. If you're not worried about preserving documents, you can simply create another Administrator account, log into it, and then delete the original one. (But if you've been working with the existing account for some time, moving the documents and other files over may not be worth it.)
In Leopard, I believe you can right click on the account in System Preferences and change the name there.