Here are the answers to the clues. (Thanks to Alconja in the Sphinx's Lair and boboquack here, for spotting #7 after I was unable to!)
1 CO. CO-IGNITIONIGNITION
2 ICON. ICON NOTING
3 CITING. CITING COON
4 COINING. COINING TOO
5 ONGOING. ONGOING TIC
6 GIN. GIN, NO TONIC
7 NOTICING. NOTICING IO
8 COTTON. COTTON I GIN
9 INTO. INTO COOING
These have
common letters INCOGNITO; and their extra letters, in order ... are also INCOGNITO. (Neat!)
So the intended final answer is
INCOGNITO (its anagram COGNITION might seem possible but note that the title also hints at INCOGNITO as answer; thanks to GPR for pointing me at this, which I had totally missed).