How can I change my screen name?
Solution 1:
Your screen name in uPlay enabled games is indeed your uPlay username, Watch_Dogs included.
Unfortunately, on PC, it's not currently possible to change your uPlay username. There have been a lot of complaints about this but the only thing Ubisoft is willing to say is "We're thinking about letting you do this at some point in the future, but have no timeframe for when you will be able to."
For example, this was yesterday:
The Uplay development team are actively working on a system that will address both these issues however, once the name change system is live you will be able to use a name of your choice instead of MIGHTY206774.
A week ago:
Once we have ironed out all the issues with the name change system, we will make it available for all our users. Until that time we thank you for your patience.
Or from 2013:
Unfortunately Uplay account usernames cannot be modified at this time. They are looking at implementing this feature in the future, but there isn't currently a time-frame on it.
On Xbox Live at least, your uPlay account is tied to your Gamertag, so changing your Gamertag will make you show up in-game as that name. However, when you access any of the uPlay menus, it will show your uPlay username instead.