So my misunderstanding was, that I thought that it would be possible to pass values via XAML to a ViewModel / POCO.

If I understand your comments correctly, I have (at least?) two options:

a) Create a DependencyProperty directly in the code-behind of my UserControl Child and pass the filename by binding. Just as if I were to use e.g. <TextBox Text={Binding ., Mode=OneWay} /> instead of my Child component.

b) Create instances of ChildViewModel in ParentViewModel and hold a property ObserveableCollection<ChildViewModel> in ParentViewModel.