For those who have been asking for this.

https://na.finalfantasyxiv.com/lodes...5e6eaa21ebf213

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Resumption of Character Renaming Service (Dec. 21)
As of Patch 6.01, changes were made to server processes to allow name changes even when servers are under heavy load. Therefore, the Character Renaming Service has been resumed.

Please note that when severs are under heavy load, you will not be able to randomly generate recommended names.

We apologize for any inconvenience this may have caused, and we thank you for your patience and understanding.