Logging Bots
So you can track that person that keeps changing their username

Invites: 8
Tags: 6
Deep logging available, as per the bot description

Invites: 364
Tags: 13
Booster logs, Invite logs, reaction logs, message logs, image logs, user join/leave logs, welcome messages, and more!

Invites: 12
Tags: 7
As well as allowing any user to post any emote, NQN allows moderators to create a special channel to log messages the bot has reposted.

Invites: 0
Tags: 4
Logs many servers into a channel named #bump

Invites: 245
Tags: 5
Configurable logs, every action you'll know it even channel's permissions overwrites.

Invites: 179
Tags: 11
Benny includes an advanced logging system that allows you to track everything that's going on in your server.

Invites: 419
Tags: 10
Mirai allows you to define an event channel where selected events are recorded. This allows you to have an easily visible log of moderation actions with their reasons. Username and nickname changes can also be logged.

Invites: 1
Tags: 4
HaileyBot's '$-modlog' command will make her log all server activities to a designated channel, allowing you to know what happened on your server while you were away.

Invites: 26
Tags: 5
Wick will log anything security related in a channel of your choosing in the most detailed way possible. It also logs any moderation acction made.