On a Mac, the "full name" is the name you enter, along with your password, when you log in. The "full name" is different from the "account name." Changing your admin name on a Mac is straightforward if you're just looking to change the full name, but changing the account name for an administrator requires a bit more care. As long as you change the name of the home folder before changing the account name, you won't run into problems.
Why You Should Back Up
Before attempting to change the admin name on a Mac, it makes sense to back up any important files
Change the Admin Name on a Mac
Changing the account's full name is easy because you don't need to make the full name match the home folder or the account name. You can complete the process either from the account itself or any administrator account.
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Go to the Apple menu, then to "System Preferences" and "Users & Groups." On earlier versions of the operating system, "Users & Groups" may be replaced with "Accounts."
On computers running macOS and OS X Sierra, El Capitan or Yosemite, click the padlock symbol and then enter a username and password combination for an administrator. Then, either control-click or right-click the name of the administrator whose full name you want to change and choose "Advanced Options." Change the name in the "Full Name" field as desired.
For OS X Mavericks or earlier, after going to "Users & Groups," choose the user in question and then change the "Full Name" field.
Changing an Administrator Account Name
For macOS and OS X Sierra, El Capitan, Yosemite, Mavericks, Mountain Lion and Lion, you must log in to a different administrator account than the one you want to change before you can change an admin name. If there isn't another administrator account, create one and log in to it.
Go to the "Users" folder. You can find this folder using the Finder menu, choosing "Go," then "Go to Folder" and then typing "Users." In "Users," locate the folder with the same account name as the administrator in question. Write down the name somewhere and write down the name you want to change it to because you'll need these later. Change the folder's name to the new name you want for the account and enter the administrator name and password for the account you are currently using when prompted.
Now go to "System Preferences" from the Apple menu and "Users & Groups." Click the padlock symbol and then enter the username and password for the admin account you're using. Control-click or right-click the name of the administrator you want to change and choose "Advanced Options." Change the "Account Name" to the new one, which should be identical to the new folder name, and change the "Home Directory" field to reflect this. Click "OK" and restart your Mac to confirm.