I keep seeing bots on Twitch with a name of the one who gave the streamer to the bot. Does that also work on the nightbot, or do they have another bot in use there are different ones, and if so. How can you rename the nightbot?
You can't rename the Nightbot.
The streamers then usually use other bots. (This is possible with Moobot, for example. https://moo.bot/docs/renaming-your-twitch-bot)