Not necessary to complicate your application. One situation when mentioning nicknames could be useful is if you plan to show your nickname in any residence support documentation if CIC will ask you to provide those.
For example, you may have used nickname instead of your real name attending job interviews, renting sublets, email communications etc. You may be asked to provide residence support docs at some point and then mentioning nickname right away in cit app form may be a good idea.
Think about it well. If you think there's a possibility to use it in an evidence later, then better to include it in app.
