Define yourself a key object that holds and compares the desired properties. In this simple case, you may use a small list whereas each index corresponds to one property. For more complex cases, you may use a Map (using property names as keys) or a dedicated class:
Function<Person,List<Object>> toKey=p -> Arrays.asList(p.getName(), p.getAge());
Having such a mapping function. you may use the simple solution:
list1.stream().map(toKey)
.flatMap(key -> list2.stream().map(toKey).filter(key::equals))
.forEach(key -> System.out.println("{name="+key.get(0)+", age="+key.get(1)+"}"));
which may lead to poor performance when you have rather large lists. When you have large lists (or can’t predict their sizes), you should use an intermediate Set to accelerate the lookup (changing the task’s time complexity from O(n²) to O(n)):
list2.stream().map(toKey)
.filter(list1.stream().map(toKey).collect(Collectors.toSet())::contains)
.forEach(key -> System.out.println("{name="+key.get(0)+", age="+key.get(1)+"}"));
In the examples above, each match gets printed. If you are only interested in whether such a match exists, you may use either:
boolean exists=list1.stream().map(toKey)
.anyMatch(key -> list2.stream().map(toKey).anyMatch(key::equals));
or
boolean exists=list2.stream().map(toKey)
.anyMatch(list1.stream().map(toKey).collect(Collectors.toSet())::contains);