From Tolkien Gateway
Slinker was Sam's name for the pathetic, whimpering side to Gollum's personality, faithful to Frodo and desperate for his approval. Gollum's 'Slinker' persona was associated with his original life as the hobbit-like creature Sméagol, long ago on the banks of the Gladden River before the Ring began to twist his mind. Slinker fought a failing fight for control of Gollum against his darker, more dangerous side, 'Stinker'. As he led Frodo and Sam into Mordor, Slinker gradually faded away, and the deadly, Ring-obsessed Stinker took over Gollum completely.