After some failed attempts, I have not found a way to make sure my teacher avatar display next to announcements I made if those announcements are copied to a new course. That's not great for teacher/student relationships because it looks like some announcement do not come from me.
However, I have found a way to include your avatar inside the announcement body, or anywhere I have access to the editor. This is what my announcements now look like:
Take a screen shot of your avatar. To get the white background I opened an announcement I recently created.
Upload that picture to a web host. I have my own website so it's easy, but maybe you can host it on your school's web host or a free host like Amazon.
Every time you create an announcement, be sure start by inserting an image and using the link to your hosted avatar picture. As long as it is hosted outside of Canvas, it will copy fine course-to-course.
If you want to make it look even nicer, first add the link then open the HTML editor and edit the code to look something like this. That "float" tag is what tells the browser to let the text flow to the right of the image.
<p style="float: left;"><img src="https://webhost.com/linktoyourimage.png" alt="Mr Bryn's Picture" width="73" height="64" /></p>
And that's it.