You can make a list like this, but you'll again have to use some serious hackery, and you'll have to use some "type by example" situations. For example:
// create the first list by using a specific "template" type.
var list = new [] { new { Name="", Phones=new[] { "" } } }.ToList();
// clear the list. The first element was just an example.
list.Clear();
// start adding "actual" values.
list.Add(new { Name = "Krishna", Phones = new[] { "555-555-5555", "666-666-6666" } });