The asterisk next to the name of an object in a project will only sometimes appear, and if they do the asterisk will not go away if you save the file as expected.
All 3 files shown here have been edited in one way or another, but only 1 file shows that it has unsaved changes. The first file you modify in a project will have the unsaved changes asterisk, and will not appear on any others. Closing and re-opening the file will make the asterisk go away but it will not appear again until the project has been closed and opened again.
The asterisk next to the name of an object in a project will only sometimes appear, and if they do the asterisk will not go away if you save the file as expected.
All 3 files shown here have been edited in one way or another, but only 1 file shows that it has unsaved changes. The first file you modify in a project will have the unsaved changes asterisk, and will not appear on any others. Closing and re-opening the file will make the asterisk go away but it will not appear again until the project has been closed and opened again.