Hello Alex,
Just making sure: Does your test user have a profile picture set AND an agent image set in PureCloud? Here's what mine looks like in my test org:
Profile picture:
Agent image:
Inside PureCloud, you'll see your "profile picture" when you send a message, but the customer will see the "agent image" if there is one. If there isn't one, then it will fall back to showing the image in the web chat configuration.
With that setup, here's what I see as agent and customer: