Yes, users with high level roles can change the name of a Twilio account via Console. This guide explains who has access to this setting, and how to make the change.

Notice: The Account Settings page in Console can only be accessed by users with the Owner or Administrator role. Users with other roles will not be able to access this page, and will instead receive an HTTP 403 error. For help changing user access levels, see Add, Remove, or Modify Users with Your Twilio Account.

Update an account name

1. Access the Account Settings page in Console.
2. If the account settings page is grayed out, click Authenticate to make changes at the bottom of the screen, and then enter your password to authenticate.
    
3. Enter the desired name in the ACCOUNT NAME field.
   
4. When finished, scroll to and click Save at the bottom of the screen.
    

How do I change the account name showing on the invoice?

Invoices show the Company Name, as added via the Billing Preferences page in Console. For help updating the company name, see How do I Update my Billing Settings.

Your Account Name will also be shown on your invoice in parenthesis. See more at Reading your Twilio Invoice.