Customize the BOT tag
Especially for incoming webhooks, it would be nice to override the BOT tag text that is shown on every message. This would allow (for instance) integrations to post to a channel as a user in the external system with the name of the system shown instead of BOT, e.g.:
someguy IRC: hello
myusername JIRA: issue comment
There would still be a visual indication that the username is associated with an integration and may not be an actual user, but the word BOT isn't always the best description of what's happening.