There is "Show Part Names" and with it enabled, everything is titled "Object 1-##".
So it is there, but it doesn't seem very effective. When you use "Input Text" to add a note, at least it doesn't change size as you zoom in/out; the part names however do increase/decrease as you zoom in/out and they clutter up the window. I don't necessarily need the entire name either, just the "##" part.
None of them look like they make an effort to place themselves onto the shapes, and it doesn't seem like it is possible to move them to relocate their position within their grouping of the shape they are connected to.
Some of them are getting grouped together and have the same name, which I'm sure is probably due to the model itself, but it would be nice if Designer could number the shapes externally from the model and make an effort to place the numbers onto the shapes themselves; at least the large shapes...
I can't remember whether or not they print, but making sure they do would be a good thing to have added as well.
On another note, it would be kinda nice to show/hide some of the shapes. Some people like to fill in the neckhole of a model of a helmet, and I like to be able to see into a mesh, which is not possible unless I export a model and edit the model itself. Then you need to unfold everything again and it is a big mess.
So maybe a Left-Click Select → Right-Click Edit Menu → Hide Group of Faces
and then you'd have a menu of the items that are hidden, and you could remove them from the group as well as being able to toggle all of them as hidden or not on and off without removing them from the hidden group.