The first thing to do is to look at your data: and it's got problems.
It looks like you are storing dates in a string format, or you couldn't get values for Paid_date like "2.42015" and "0" - neither of which are valid for DATETIME fields. And string based dates are a pain to work with - easy to insert, if you are lazy, but a nightmare to use every single time later.
So change your database, and use appropriate data type for each column. I'd also recommend creating a "users" table to hold the user names ("Anup", "Naveen" and so forth) and only store the ID reference in your main table. That way, you can have two people with similar or identical names and it won't mess up your data - and you don't waste space storing duplicate information. SQL is very good at relating such information!
Then it's a relatively simple bit of SQL to get your desired rows, JOIN with a GROUP subquery will do it easily:
SELECT t.*
FROM Paid_Table t
JOIN (
SELECT name, MAX(Paid_date) AS Paid_Date
FROM Paid_Table
GROUP BY name) AS t2
ON t.name = t2.name AND t.Paid_Date = t2.Paid_Date
But with strings? Horribly complex, I'm afraid.