Not really sure what you are asking. There should not be anything preventing it from working with other addons. If it’s giving you a specific error, I can look into why it’s not compatible. If you are asking if it does something different when you have an unrelated third party addon installed (that I know nothing about), no, it doesn’t do anything differently based on things you have installed.
If your addon does something to change their username, the question is best suited for that addon (if you want it to make changes to something else like display name). This addon doesn’t have any control over actions other addons make, so if your inquiry is based on an action a different addon is making, that addon should also be the decider about what changes when that action is performed.
TL;DR: it’s going to be simpler for that addon to make whatever changes it wants to make rather than expect that addon to notify my addon that it performed some random action.