The standard Date-Time classes do not have any attribute to hold the formatting information. Even if some library or custom class promises to do so, it is breaking the Single Responsibility Principle. A Date-Time object is supposed to store the information about Date, Time, Timezone etc., not about the formatting. The only way to represent a Date-Time object in the desired format is by formatting it into a String using a Date-Time parsing/formatting type:
- For the modern Date-Time API: java.time.format.DateTimeFormatter
- For the legacy Date-Time API: java.text.SimpleDateFormat
Note that the java.util Date-Time API and their formatting API, SimpleDateFormat are outdated and error-prone. It is recommended to stop using them completely and switch to the modern Date-Time API*, released in March 2014 as part of Java SE 8 standard library.
Apart from that, there are many things wrong with your code:
- Using Y( Week year) instead ofy(Year). Check the documentation to learn more about it.
- Not using LocalewithSimpleDateFormat. Check Never use SimpleDateFormat or DateTimeFormatter without a Locale to learn more about it.
- Enclosing Zwithin single quotes means it is just a character literal with no meaning other than representing the letterZ. The pattern,yyyy-MM-dd'T'HH:mm:ss.SSS'Z'should beyyyy-MM-dd'T'HH:mm:ss.SSSXXX.
Solution using java.time, the modern Date-Time API:
import java.time.OffsetDateTime;
import java.time.format.DateTimeFormatter;
import java.util.Locale;
public class Main {
    public static void main(String[] args) {
        var dateString = "2021-05-12T12:12:12.121Z";
        var odt = OffsetDateTime.parse(dateString);
        var dtf = DateTimeFormatter.ofPattern("MMM dd, uuuu", Locale.ENGLISH);
        System.out.println(dtf.format(odt));
    }
}
Output:
May 12, 2021
ONLINE DEMO
Here, you can use y instead of u but I prefer u to y.
Learn more about the modern Date-Time API from Trail: Date Time.
* For any reason, if you have to stick to Java 6 or Java 7, you can use ThreeTen-Backport which backports most of the java.time functionality to Java 6 & 7. If you are working for an Android project and your Android API level is still not compliant with Java-8, check Java 8+ APIs available through desugaring and How to use ThreeTenABP in Android Project.