I have already converted the above to hashmap. 
I would suggest you don't do that. I suggest you convert it to a List<Person> where each Person has a name, date and ID. (If not Person then some other class.) It makes more sense as a list than a map, because that's really what the JSON shows: a list of objects, each of which has a name, date and ID. I'd personally make the date a java.time.Instant or something similar, but that's a separate matter.
At that point, all you need to do is either implement a Comparator<Person> that compares objects by date, or make Person implement Comparable<Person> in the same way. Using a separate Comparator<Person> feels more appropriate in this case, as it seems equally reasonable to sort a List<Person> by name or ID. Then you just need to call Collections.sort(people, comparator) and you're done. There are plenty of examples on Stack Overflow to help you sort by a particular property.
The key part is to realize that what you've got isn't naturally a map - it's a list.