There doesn't appear to be a way to rename a virtual agent as of right now.
This has been completed, please see:
I would like to change the Icon as well.
Can we change this chap?
Unfortunately, no. Can't change that icon either. But there is customization/theming of bot in the roadmap. Thanks.
Hi @HaydenSinclair ,
I already create the idea here: https://powerusers.microsoft.com/t5/Power-Apps-Ideas/Change-the-bot-icon-Power-Virtual-Agents/idi-p/...
We are working on a blog called "Change your Power Virtual Agents Web Chat bot icon and name" which will come out soon. Stay tuned!
Here is the forum announcement for the blog.