Get nested generic type object's property and attribute values through Reflection at run time

I created a custom attribute class

    [AttributeUsage(AttributeTargets.Property)]
    public class MyCustomAttribute : Attribute
    {
       public string Name{ get; set; }
    }

I have a complex nested object below:

    public class Parent
    {
       [MyCustom(Name = "Parent property 1")]
       public string ParentProperty1 { get; set; }

       [MyCustom(Name = "Parent property 2")]
       public string ParentProperty2 { get; set; }

       public Child ChildObject { get; set; }
    }

    public class Child
    {
        [MyCustom(Name = "Child property 1")]
        public string ChildPropery1 { get; set; }

        [MyCustom(Name = "Child property 2")]
        public string ChildProperty2 { get; set; }
    }

I want to get the list of property names, attribute name value for each property if this object is passed in as a generic object at run time, how can I do this?

I know how to do this for a flat structure generic object using the code below, but I'm unsure how to retrieve all nested object property and attribute, do I need to use some sort of recursive function?

public void GetObjectInfo<T>(T object)
{
   //Get the object list of properties.
   var properties = typeof(T).GetProperties(BindingFlags.Public | BindingFlags.Instance);

   foreach (var property in properties)
   {
      //Get the attribute object of each property.
      var attribute = property.GetCustomAttribute<MyCustomAttribute>();
   }
}

Note, the object I used is a very simplistic version of what is in real life, I could have multiple level of nested child or nested list/array ect..