When I send a test sms from https://www.twilio.com/user/account/developer-tools/api-explorer/message-create with a predefined friendly name, it doesnt apear on my phone. I only see the number. -if this isnt possible, do you know other providers with this function that work?
[UPDATE]: Twilio now supports this feature.
You can now send messages from an alphanumeric sender ID using Twilio. I wrote up a blog post on how you can achieve this in Ruby and you can check out this article on how to get started with an alphanumeric sender ID on Twilio for more of an overview. Then check out the documentation on how to send an SMS message from an alphanumeric ID.
[UPDATE] Previous answer is below.
Twilio developer evangelist here.
You're absolutely right, the friendly name defined in your account is actually for your uses only and is not intended to appear in place of the number when sending an SMS. We have a few reasons for this, which might be interesting to you depending on your use case.
I don't have a particular company that I can recommend that does allow you to do this. A Google search might help though.