When composing a message on the Send Message page, you can adjust settings/options for each endpoint on-the-fly. This allows you to change options, such as the SMS "From name", for the current message.
To adjust an endpoint's option, simply click on that endpoint's name in the list of endpoints (Step 2) of the composer window.
Then adjust the selected endpoint's options according to your needs. (The options shown in your view will vary depending on which endpoint you're adjusting, your login permissions, and your local settings/options, of course.)