One of the goals in the faction card says to recruit a named NPC without letting anyone except maybe the recruit know that the PC is a member of the Court.
My question is: Would the PCs from other factions recognize members of the Court and are they exempted from the "not letting anyone know" restriction.
Only if your character tells them or wears some obvious marking. Their players may know, such as by reading the sign-in sheet.
No, this doesn't exclude members of your party. They're precisely who you're supposed to conceal your faction from. It's intended that you can't usually get members of other factions to help with your Sovereign Court business, unless you're clever about it.