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This is a function of the client. You can't set it on the server. MySQL ships with a client, and a server. The client determines the prompt. There is nothing you can do on the server to fix that. The client could be something totally different that has for its prompt
You can see the code here
construct_prompt(). Nothing there hits the server. That said, it gets set here in the main
default_prompt = my_strdup(getenv("MYSQL_PS1") ?
"\\N [\\d]> ",MYF(MY_WME));
current_prompt = my_strdup(default_prompt,MYF(MY_WME));
So it would seem you could set it through the
MYSQL_PS1 environmental variable.