Mentioning a server name once only counts as soft advertising. We warn for it then mute for 1 hour if the player continues.
Yet this applies to global chat, not private chat.
It's when IPs are spammed deliberately that is when we perm ban players. It has to be in global chat or something extreme like tping to everyone and putting it in their plot chat etc.
So no, this case would not be punishable with a ban. But if you believe the player did more than this screenshot I can look into it for you.