To change your picture, log into Moodle then click your name in the top right of the screen → Profile → Edit Profile and scroll down to the User Picture area. Drag your desired image file into the New Picture box. The file should be a .jpg or .png file format and will be cropped and resized to a 100x100 pixel square automatically.
Pictures are loaded from Banner in the Fall. If you have loaded a different picture into Moodle it won't be overwritten, but if you have deleted your picture from Moodle, your ID picture will be reloaded into your profile.