How your practice name appears at the bottom of the SMS is taken from SystmOne. (Note: if your practice uses EMIS, please follow the steps in this article.)
To change your practice name in your text messages:
1. In SystmOne, click 'Setup' in the blue ribbon along the top of the window. Then, click 'Users & Policy' followed by 'Organisation Details'
2. In the Name field of the window that appears, edit your practice name and click 'OK' at the bottom to save it
3. When the pop up below appears, click 'Yes' one the timer has finished
4. You will normally need to close and reopen SystmOne and Accurx Desktop to see the changes applied.
If you wish to change who the message appears from on the patient's phone see here.