You were almost correct with groupingBy, but the second parameter of that is a Collector, not a Function. Thus I used toMap.

 Map<String, Integer> map = Stream.of("bla", "blabla", "blablabla").distinct()
            .collect(Collectors.toMap(Function.identity(), String::length));

Lets track it down:

The way you have initiated:

List<Map<String, String>> myList = new ArrayList<Map<String, String>>();

So you have a list of maps.

Now how do we get an item from a List, there are two ways:

for(int index = 0 ; index < myList.size() ; index++){
    Map<String, String> listItem = myList.get(index);
    // Iterate over the map.
}

or

for(Map<String, String> listItem : myList){
    // Iterate over the map.
}

Now how do we iterate over the map:

Iterator it = listItem.entrySet().iterator();
while (it.hasNext()) {
    Map.Entry pair = (Map.Entry)it.next();
    System.out.println(pair.getKey() + " = " + pair.getValue());
}

    Map<String, List<String>> myMaps = new HashMap<String, List<String>>();
    for (DataObject item : myList) {
        if (!myMaps.containsKey(item.getKey())) {
            myMaps.put(item.getKey(), new ArrayList<String>());
        }
        myMaps.get(item.getKey()).add(item.getValue());
    }

You can create a class Company and then subsequent operations become much simpler.

class Company {
    String company;
    String billType;
    String billPeriod;

    public Company(String company, String billType, String billPeriod) {
        this.company = company;
        this.billType = billType;
        this.billPeriod = billPeriod;
    }

    // getters, setters, toString, etc
}

Initialize the list :

List<Company> list = new ArrayList<>();
list.add(new Company("LG", "A", "09-2018"));
list.add(new Company("LG", "A", "09-2018"));
list.add(new Company("LG", "A", "09-2018"));
list.add(new Company("LG", "B", "01-2019"));
list.add(new Company("LG", "B", "01-2019"));
list.add(new Company("Samsung", "A", "10-2018"));
list.add(new Company("Samsung", "A", "10-2018"));
list.add(new Company("Samsung", "B", "11-2018"));

Now for an example, you can group by company name :

Map<String, Long> map = list.stream().collect(
        Collectors.groupingBy(Company::getCompany, 
                              Collectors.mapping((Company c) -> c, Collectors.counting())));

Now it becomes much easier to perform other operations as you desire. Also, here instead of creating 8 maps you end up dealing with just 1 list.

You can use the groupingBy method to manage aggregation, for example:

public static void main(String[] args) {
    List<String> list = Arrays.asList("A", "B", "C", "D", "A");
    Map<String, List<String>> map = list.stream().collect(Collectors.groupingBy(Function.identity()));
}

If you want more flexibility (for example to map the value and return a Set instead of a List) you can always use the groupingBy method with more parameters as specified in javadoc:

Map<City, Set<String>> namesByCity = people.stream().collect(Collectors.groupingBy(Person::getCity, mapping(Person::getLastName, toSet())));

Because you have only one entry, then in this case, you need just to focus on the values, and for the key you can just use "1", for that you can create a Map like this :

Map<String, List<String>> result = new HashMap<>();
result.put("1", list.stream()
        .filter(e -> e.containsKey("1"))
        .flatMap(e -> e.values().stream())
        .flatMap(List::stream)
        .collect(Collectors.toList()));

Or as stated by Lino in the comment, you can also use :

Map<String, List<String>> result = list.stream()
    .filter(e -> e.containsKey("1"))
    .flatMap(e -> e.values().stream())
    .flatMap(List::stream)
    .collect(Collectors.groupingBy(t -> "1"));

You can use groupingBy collector with mapping downstream as :

Map<String, List<Result>> map = data.stream()
        .collect(Collectors.groupingBy(a -> a.getSystemId() + ":" + a.getFileName()
                , Collectors.mapping(a -> new Result(a.getX(), a.getY()),
                        Collectors.toList())));

I think what you have there is fine, assuming \\. matches the single character ..

However, you can clean it up a bit by compiling the regex into a Pattern and using Stream#map:

Pattern pattern = Pattern.compile("[.]");

Arrays.asList("Stack.Overflow")
      .stream()
      .map(pattern::split)
      .collect(Collectors.toMap(s -> s[0], s -> s[1]));

Output:

{Stack=Overflow}

Split the elements of the List and collect to Map:

Map<String,String> map = 
    list.stream()
        .map(s -> s.split("="))
        .collect(Collectors.toMap(a->a[0], a->a[1]));

Note that if the key should be an Integer, you'll have to change a[0] to Integer.valueOf(a[0]).

Also note that if the List may contain duplicate keys, you should decide how to handle them (and possibly add a merge function to the collector).

I believe something like this should work:

Map<String,List<String>> map =
    userList.stream()
            .flatMap(user -> {
                Map<String,String> um = new HashMap<>();
                um.put("names",user.getName());
                um.put("age",user.getAge());
                um.put("org",user.getOrg());
                return um.entrySet().stream();
            }) // produces a Stream<Map.Entry<String,String>>
            .collect(Collectors.groupingBy(Map.Entry::getKey,
                                           Collectors.mapping(Map.Entry::getValue,
                                                              Collectors.toList())));

It converts each User to a Map<String,String> (containing the 3 required properties indexed by the required keys), and then groups the entries of all the user maps by their keys.

EDIT:

Here's another alternative that creates the Map.Entrys directly instead of creating the small HashMaps, so it should be more efficient:

Map<String,List<String>> map =
    userList.stream()
            .flatMap (user -> Stream.of (new SimpleEntry<>("names",user.getName()),
                                         new SimpleEntry<>("age",user.getAge()),
                                         new SimpleEntry<>("org",user.getOrg())))
            .collect(Collectors.groupingBy(Map.Entry::getKey,
                                           Collectors.mapping(Map.Entry::getValue,
                                                              Collectors.toList())));

You may do it like so:

Map<String, List<String>> locationMap = locations.stream()
        .map(s -> s.split(":"))
        .collect(Collectors.groupingBy(a -> a[0],
                Collectors.mapping(a -> a[1], Collectors.toList())));

A much more better approach would be,

private static final Pattern DELIMITER = Pattern.compile(":");

Map<String, List<String>> locationMap = locations.stream()
    .map(s -> DELIMITER.splitAsStream(s).toArray(String[]::new))
        .collect(Collectors.groupingBy(a -> a[0], 
            Collectors.mapping(a -> a[1], Collectors.toList())));

Update

As per the following comment, this can be further simplified to,

Map<String, List<String>> locationMap = locations.stream().map(DELIMITER::split)
    .collect(Collectors.groupingBy(a -> a[0], 
        Collectors.mapping(a -> a[1], Collectors.toList())));