Other than under the menu, I don’t think that’s an option unless you try and get fancy with coding, etc. Not sure you would-be able to use the short codes so if you find a way it’s likely pulling from other source...

Can confirm, other than external workarounds (using an embedded widget that is doing a quick api call on page load to get current user, no way to do this. I do use it for things like embeded support/surveys and such (have a couple writeups on this), but have found it not worth the effort of setup just for basic personalization on a home page.

Check out this post, maybe this is something that you could leverage

This is a fun hack around, just keep in mind if using mobile they will see the widget as is without modifications, but totally depends on your use of mobile or not.