API v21 added a renameAccount() method to the AccountManager, if that helps.
From the docs:
This is equivalent to removing the existing account and adding a new
renamed account with the old account's user data.
That means for backward compatibility, you would have to manually remove the account and run through the same procedure as creating a new one (AccountManager.addAccountExplicitly() and AccountManager.setUserData()) afterwards.
Edit:
If you want to update your contacts afterwards to display the correct account name, try this (untested) code:
ContentValues contentValues = new ContentValues();
contentValues.put(ContactsContract.RawContacts.ACCOUNT_NAME, "new account name");
getContext().getContentResolver().update(ContactsContract.RawContacts.CONTENT_URI,
contentValues,
ContactsContract.RawContacts.ACCOUNT_TYPE + " = ? AND " + ContactsContract.RawContacts.ACCOUNT_NAME + " = ?",
new String[]{"your account type", "old account name"});