If your key is NOT guaranteed to be unique for all elements in the list, you should convert it to a Map<String, List<Choice>> instead of a Map<String, Choice>

Map<String, List<Choice>> result =
 choices.stream().collect(Collectors.groupingBy(Choice::getName));

You have to sort with a custom comparator based on the value of the entry. Then select all the keys before collecting

countByType.entrySet()
           .stream()
           .sorted((e1, e2) -> e1.getValue().compareTo(e2.getValue())) // custom Comparator
           .map(e -> e.getKey())
           .collect(Collectors.toList());

You could do it without streams, yet in a modern fashion, as follows:

Map<String, List<Object>> result = new HashMap<>();
data.forEach(element -> 
    element.forEach((k, v) - > 
        result.computeIfAbsent(k, x -> new ArrayList<>()).add(v)));

This iterates the list and then each map and uses Map.computeIfAbsent to accomodate entries in the result map.

Below code should work for you:

package com.shree.test;

import java.util.AbstractMap;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Map;
import java.util.stream.Collectors;

public class StreamTest {
    public static void main(String[] args) {
        String[] myStringArray = {"TITLE1", "TITLE2", "TITLE3"};
        List<String> pages = new ArrayList<>();
        pages.add("TEXT,TITLE2,TEXT,ONE,TWO");
        pages.add("TEXT,TITLE1,TEXT,ONE,TWO");
        pages.add("TEXT,TITLE2,TEXT,ONE,TWO");
        pages.add("TEXT,TITLE2,TEXT,TITLE3,TWO");
        pages.add("TEXT,TITLE3,TEXT,ONE,TWO");



         Map<Object, Object> titleMap = getTitleMap(myStringArray, pages);

         titleMap.entrySet().forEach(System.out::println);
    }

    private static Map<Object, Object> getTitleMap(String[] myStringArray, List<String> pages) {
        Map<Object, Object> titleMap = Arrays.asList(myStringArray).stream()
            .map(
                    (title)->{
                        return new AbstractMap.SimpleEntry<>(title, pages.stream()
                                .filter((page)->page.contains(title))
                                .collect(Collectors.toList()));
                    }
                )
            .collect(Collectors.toMap(entry->entry.getKey(), entry->entry.getValue()));
        return titleMap;
    }
}

The great answer above can further be improved by method reference notation:

List<Dog> dogs = ...
Map<String, List<Dog>> map = dogs.stream()
     .collect(Collectors.groupingBy(Dog::getBreed)); 

To obtain the same result of your iterative code

List< PublicationSession> publicationsToFilter = new ArrayList<>();
for (List< PublicationSession> sessions : effectiveDatePublicationMap.values()) {
    publicationsToFilter.addAll(sessions);
}

with streams you first have to use flatMap to transoform your stream of List<PublicationSession> in a stream of PublicationSession, and then collect all of them in a list with collect(Collectors.toList())

List<PublicationSession> publicationsToFilter = effectiveDatePublicationMap.values()
                                                   .flatMap(Collection::stream)
                                                   .collect(Collectors.toList());

Before collecting the result, you can filter or sort as you wish.