You can use SimpleDateFormat to convert between a String and a Date object and vice versa based on a pattern. Click the API link, you'll see patterns being explained in detail. A 4-digit year can be represented with yyyy, a 3-character month abbreviation can be represented with MMM and so on.
First you need to parse the String of the first format into a Date object:
SimpleDateFormat sdf1 = new SimpleDateFormat("yyyy-MM-dd HH:mm:ss.SSS");
Date date = sdf1.parse(inputString);
Then you need to format the Date into a String of the second format:
SimpleDateFormat sdf2 = new SimpleDateFormat("dd-MMM-yyyy", Locale.ENGLISH);
String outputString = sdf2.format(date);
Note that you need to take the Locale into account as well to get the month to be printed in English, else it will use the platform's default locale to translate the month.