I just found this out after looking around for a while. this method works as of 2019-May 30th, on Chrome 74. Other versions may change how it's done.
1) Open Chrome, make sure you are on the profile you want to change the name or icon picture of.
- Change profiles by clicking on the icon on the upper right of Chrome, it is the second to last thing on upper right, just before the 3 dots / menu button.
2) Once you're the profile to edit, click on the menu (the 3 dots on upper right) and click on 'Settings' at the bottom of the list (just above 'Help')
3) The top Settings box is for 'People'. The third line is 'Chrome name and picture'. Click that line.
4) You should see the settings window show 'Edit person' with a line to change the profile name and the icon. To finish and save any changes, click on the back (left pointing) arrow next to the words 'Edit person'