You can't use a method reference for a constructor that needs to receive a free variable, i.e. a variable from the context.
Please refer to the Java Tutorial, section Method References to find more info about method references.
You can use a lambda expression instead:
Mapper mapper = new Mapper(); List<Store> actions = names.stream() .map(name -> new Store(name, mapper)) .collect(Collectors.toList());
If, for whatever reason, you insist on using a method reference, you still can, though the solution is more complex and cumbersome. In fact, it's much better from all possible points of view to use a lambda expression instead of the hack I'm introducing below. I'm writing it just to show that method references are good only if you already have a method or constructor whose signature matches the expected one.
Suppose you declare this helper method:
public static <T, U, R> Function<T, R> bindSecond( BiFunction<T, U, R> biFunction, U free) { return t -> biFunction.apply(t, free); }
Here I'm are creating and returning a 1-argument function that applies its only one argument to the given bifunction (a 2-argument function), as well as the given free variable. In other words, I'm binding the given free variable to the given bifunction as its second argument.
In your example, Store::new is actually a bifunction that takes two arguments (name and mapper) and returns a value (the new Store instance), and you are getting that compilation error because Stream.map expects a 1-argument function that takes the element of the stream as its only one parameter.
The bindSecond helper method actually transforms the given bifunction and free variable into a 1-argument function that matches the signature of the Stream.map method.
You could use it as follows:
Mapper mapper = new Mapper(); List<Store> actions = names.stream() .map(bindSecond(Store::new, mapper)) .collect(Collectors.toList());
But again, I see no point in using this over a simple lambda expression.
public Store(String name) { this(name, new Mapper()); }