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Can you change a game name with ubisoft, does it cost , I'd like to change it, does it take a few weeks to do ?, or can be done straight away.
You can change your Ubisoft Account username here: https://account.ubisoft.com/en-GB/account-information.
As BB-Ghost mentioned, you can change it every 30 days. Have in mind that your PlayStation display username could be different and that one should be changed through PSN account management.