I see this issue as well.
Really, when possible, I think the bot name should be decoupled from the server name, anyway. They are different things, after all.
Putting things practically, it isn't quite right if I have to name the server itself "pz-chat" just so the bot can represent itself properly in my Discord server. Can we have the bot name-able in the server config?
As a workaround, you can adapt this command to call a bot nickname change. You'd want to run this every time your server has finished starting. There is also a lockout for bot nickname changes after I think three times within so many minutes, just as a warning. Server start = 1, so you have a couple more tries.
curl -H 'Authorization: Bot your_bot_token_here' -H "Content-Type: application/json" -X PATCH -d '{"username": "your_bot_name_here"}' https://discordapp.com/api/users/@me