Both implementations are incorrect as they needlessly mutate the input list:

  List<String> namesNotStartingWithB = new ArrayList<>();
  for (String name : names) {
      if (!name.startsWith("B")) {
          namesNotStartingWithB.add(name);
      }
  }

Imagine a scenario where you're filtering one of the arguments to a method: the input will be mutated with no indication to the caller (or in the method signature), causing bugs, iterator invalidation etc.