May be I am not able to explain properly. When you use a component within a component(in your case featureMedia is used inside clientTestimonials), it ask for a name you want to put within that component and the component itself.
let me give you an example what I have. So here is the component which uses pricing component
Now when I click on the pricing component, I see below screen
Here the name of the component is pricing(which is displaying under select a component) and the name which is being used in the asset pricing is also pricing(displaying under Name field). I was asking you to change the name (in Name) field under one of the component.
Also on another note, please check your collection names in schema files if its not duplicated.