Can Twilio 'from' number be a text field with the organisation name?
Yes, it's easy. You have to ask Twilio customer support to enable 'Alphanumeric Sender ID' in your project.  Here's the link for that.  Once that's done then all you need to do is to set the 'From=' in Administer/Settings/SMS Providers to whatever you want.  Of course, users cannot then reply or 'STOP' etc.  But it works and there's nothing to enter or change in your Twilio account once the alphanumeric send ID is enabled, just update Civi with your chosen text.