i found the way to check is the value contains in simple array :
var filter = Builders.Filter.AnyEq(x => x.Tags, \"mongodb\");
You need the $elemMatch operator. You could use Builders.Filter.ElemMatch or an Any expression:
$elemMatch
Builders.Filter.ElemMatch
Any
Find(x => x.Tags.Any(t => t.Name == "test")).ToListAsync()
http://mongodb.github.io/mongo-csharp-driver/2.0/reference/driver/expressions/#elemmatch