For on demand.
1) From test or Dev go into the UI make a copy and start changing things.
Top icon in far left is the element. #ppm_header_user_img
It's in base64. Take your sized image Roughly 16x16px and convert it(Google image to base64).
Then comment out the old code and post yours in. Save and refresh.
#ppm_header_user_img {
background: url(data:image/png;base64,iVBORw0KGg..............);
2) Train users? Or Inspect element and find the bar and add some image code in the compiling function. On Demand will be unable to modify the underlying JS files and functions. I'm sure it is not advised for on premise, as any updates might wipe it out/ cause issues.