Obtain the list of field names as strings for a given type that has nested collections inside recursively C#

Some of the classes I have are as follow:

public class ObjectA
{
    List <ObjectB> BCollection {get; set;}
}
public class ObjectB
{
    String Name {get;set;}
    List <ObjectC> CCollection {get; set;}
}
public class ObjectC
{
    String Name {get; set;}
}

I need a method that recursively analyses the object and returns the list of field names as List. So that the list would contain:

ObjectA.BCollection,
ObjectA.BCollection.ObjectB.Name,
ObjectA.BCollection.ObjectB.CCollection,
ObjectA.BCollection.ObjectB.CCollection.ObjectC.Name.

The important thing is that at run time I do not know the type, I need to get the field names using reflection.