I have more than one user in Chrome Browser (chrome://settings/ Add new user) and can't find out how to specify a custom icon for each user. Chrome allow me select an icon from a list of icons set, but I want set my own image.
Google Chrome OS
If you are talking about changing a user account picture on Chrome OS (Google's operating system), a simple search will find that information for you on Google's Help site. Below is from the previous link.
Google Chrome Browser
To change an account picture on Google Chrome (the browser), follow the directions below:
At this time is it not possible to use your own custom picture in Google Chrome, but it is possible to use your own custom picture in Chromium as per this link. This Superuser question asked the same question, but at the time, the answer was "no". Now the answer is "yes", but only for Chromium.
Set to 'enabled' and relaunch. That will bring the new right-corner username menu with name instead of image. But now going back to the same address and setting that to 'disabled', then relaunching, will show the Google account user image instead of the avatar, or that image will become available among the avatar images.
(It's like a bug: going directly from 'default to 'disabled' will not work. You have to go from default to enabled, relaunch and then disable and relaunch.)