There might be an option for this under the Project Options controls. I don't use this so I can't say what issues you may or may not run into. It doesn't look like it is specific to ports since it says local nets.
I'm sure you know it but another way to make this a bit more obvious to a reviewer is to have a top level sheet that shows the other sheets and their interconnections. That provides the mapping on signal names that go between sheets.
After reading a little more about this here.... https://www.altium.com/documentation/altium-designer/workspacemanager-dlg-projectpropertiesdialog-pagecontrol-main-optio…
.....I'm thinking my suggestion is not going to work. But it is an interesting question so now I have to figure it out.
So, I found this old thread that mentions how to do this as a hidden method.
Also, for AD there is this YT tutorial but the exact commands don't work with CS but it does give some clues. https://www.youtube.com/watch?v=3mpfB3EG5wo
In one of my schematics, I set my Project Options to be Net Identifier Scope as Flat (Only ports global).
Then I had to compile the project by right click on the project name in the navigation pane (also F9).
Then type in the search box the partial word "refer" to bring up context sensitive help.
This does add some sheet names but they are not quite what I would want.
Using the YT video, we can find the options to control how this is displayed. You will have to play with this on your own from here.
I found that setting sheet style to number and location style to none puts a simple number next to the port symbol and that shows the sheet it references. I only have two sheets on the schematic I tested so your mileage may vary with 10 sheets.