LINQ to Entities how to update a record

Just modify one of the returned entities:

Customer c = (from x in dataBase.Customers
             where x.Name == "Test"
             select x).First();
c.Name = "New Name";
dataBase.SaveChanges();

Note, you can only update an entity (something that extends EntityObject, not something that you have projected using something like select new CustomObject{Name = x.Name}