Yes, absolutely. Please go to Menu → Settings → Messages → Tap on a message → Template. You can change the text and the dynamic fields that get automatically filled in for the appointment.
The length of your message is dynamic and depends on the text and fields you’re using. The standard length of a text message is 160 characters, but using Unicode characters (Emojis or special characters) will decrease this length to 70 characters only, thus consuming more text messages in order to send the reminder.