You can use this as a start to your edit validate. It will match the pattern you described.
You can tune it from here depending on your business requirement. I've currently made it case insensitive and also some assumptions on what a minimum name should be.
(Maybe you literally want to check for capitalization, etc.)
boolean retval = false;
String firstName = "((?:[a-z][a-z]+))"; // Name 1 assumes at least two characters
String dot = "(\\.)"; // A literal dot
String middleI = "([a-z])"; // Any Single Character for middle name
String lastName = "((?:[a-z][a-z]+))"; // Last name assumes at least two characters
java.util.regex.Pattern p = java.util.regex.Pattern.compile(firstName+dot+middleI+dot+lastName, java.util.regex.Pattern.CASE_INSENSITIVE);
java.util.regex.Matcher m = p.matcher(theValue);
retval = m.matches();