You need Distinct
and Select
.
var newList = list.Select(x => x.Name).Distinct().ToList();
If you also want your original class, you would have to get a bit more fancy.
Either get MoreLINQ and use its DistinctBy
method:
var newList = list.DistinctBy(x => x.Name).ToList();
Or use a clever GroupBy
hack:
var newList = list.GroupBy(x => x.Name).Select(x => x.First());