I suppose your name attribute is of
String type, so if you've all the names as a list (ArrayList/Vector), you're in luck, just use Collections.sort() and it would sort it in ascending order by natural order (in this case, your requirements).
However, if you need it in descending order, you'd have to write your own comparator. Also note that the ascending order may not be what same users expect. For e.g., is "AAA" before or after "aaa", it's pretty subjective here.
Now, if you've overriden your POJO's equals & hashCode methods, you'll just need to implement a Comparator class, pass in the list of POJOs together with the comparator to Collections.sort() and get it done.
Not sure which method would be better in performance though.