we call this the Record Preview Panel, although some people might call it the hover panel. Currently it shows the first 5 fields of the Compact Layout for an object, except for Accounts and Contacts where it also shows 2 related lists that are hardcoded. You can change the compact layout to change which fields are displayed, which is different from Classic, which used the mini layout.

It's on the roadmap to extend customizability of the hovers to admins, similar to how admins can use the lightning app builder to customize record and other pages within the app to add components, rearrange, etc.