It's still the embedded FamilySearch ID. Tools>File Options>General>"Number to display after name" does have the option to display the FamilySearch ID. If you select None or FamilySearch ID you will see still the FamilySearch ID after the matched person's name on the Edit Person screen. If you change it to Record Number or Reference Number it will show the number and the FamilySearch ID afterwards. You won't see the behavior on the Pedigree, Family, Descendant, etc Views. Its only when you open the Edit Person screen or the FamilySearch Person Tools that you will see the embedded FamilySearch ID.
The only way to not show the FamilySearch ID for people in your database matched to someone on Family Tree, is to go to Tools>File Options>FamilySearch>and uncheck "Enable FamilySearch Support". But, then you wouldn't be able to use the FamilySearch Person Tools any more.
It's only if you set Tools>File Options>General>"Number to display after name" to FamilySearch ID that you will see it print out on any reports. It's rather harmless to have the number after a person's name on the Edit Person screen. It's just for your reference. On the Edit Person screen if you click on Options you will see "Put FamilySearch ID on clipboard". It's referencing the number after that person's name on that screen.