Refactoring String manipulating method with TDD
Often, when performing text manipulation, Regular Expressions can do the work for you. Your solution is essentially manually building a text parser and stripper, when a regular expression will do the work in a much more concise way.

The regular expression would be to remove all text up to the last \ or ; character, which would be written as:

private String extractSimplePromptName(String promptNameOrg) {
    return promptNameOrg == null ? "" : promptNameOrg.replaceAll("^.*(\\\\|;)", "");
}