Use the Power of Objects

The usage of maps in your code is an example of abuse of collections. Storing the data in such a way is inconvenient and error-prone.

Instead of trying to substitute a domain object with a Map, you need to define a class (or a record).

It'll give you many advantages that you're depriving yourself by using maps:

• Ability to use the proper type for every property instead of keeping everything as strings;
• No need to perform parsing;
• Self-explanatory method names instead of hard-coded string keys, and your code will not fail because you've misspelled a key;
• The code is easier to read and maintain.

For the sake of simplicity and conciseness, I'll go with a Java 16 record:

public record Person(String name, int age) {}

And now we have two lists of Person instead of two lists of maps.

To implement the logic when we're starting with examining the first list and only if a result was not found we proceed by iterating through the second list, we can make use of the Java 9 method or() defined by Optional. While invoked on the optional object containing a value, or() returns the same optional, otherwise it'll return an optional produced by a supplier provided as an argument.

For convenience, we can define a method that takes a List<Person> and the target age and returns an optional result.

public static Optional<Person> getPersonByAge(List<Person> people, int age) {
    return people.stream().filter(pers -> pers.age() == age).findFirst();
}

We can make this method reusable by making it generic. So it would expect a List<T> and a Predicate<T> as its arguments.

public static <T> Optional<T> getPersonByAge(List<T> people,
                                             Predicate<T> predicate) {
    
    return people.stream().filter(predicate).findFirst();
}

And that how we can apply it:

List<Person> list1 = List.of(new Person("john", 30), new Person("marry", 31));
List<Person> list2 = List.of(new Person("mike", 40), new Person("terry", 41));
        
Predicate<Person> age40 = pers -> pers.age() == 40;
    
String name = getPersonByAge(list1, age40)
    .or(() -> getPersonByAge(list2, age40))
    .orElseThrow()
    .name();
    
System.out.println(name);

Output:

mike

A link to Online Demo

If you want to use the map so you can:

Optional<String> nameByAge = getNameByAge(list1, "40").or(()->getNameByAge(list2, "40"));

public static Optional<String> getNameByAge(List<Map<String, String>> people, String age) {
        return people.stream().filter(person -> person.get("age").equals(age)).findAny().map(person-> person.get("name"));
    }