LINQ return items in a List that matches any Names (string) in another list

var products = shopProducts.Where(p => listOfProducts.Any(l => p.Name == l.Name))
                           .ToList();

For LINQ-to-Objects, if listOfProducts contains many items then you might get better performance if you create a HashSet<T> containing all the required names and then use that in your query. HashSet<T> has O(1) lookup performance compared to O(n) for an arbitrary IEnumerable<T>.

var names = new HashSet<string>(listOfProducts.Select(p => p.Name));
var products = shopProducts.Where(p => names.Contains(p.Name))
                           .ToList();

For LINQ-to-SQL, I would expect (hope?) that the provider could optimise the generated SQL automatically without needing any manual tweaking of the query.