Hi Julie.
you should only copy your Own icon in your site theme folder, then change the icon name to name of moodle icon that exists there. Thats it!
Replace ../moodle/theme/[yourchosentheme]/favicon.ico with a new favicon.ico that you have created from your own image file.
Here are some favicon generator sites that will turn a regular image into a favicon for you:
Here are some favicon generator sites that will turn a regular image into a favicon for you: