I'll preface this by saying I have no idea how much the movies changed from the books, but during all 3, Gollum is very consistently characterised:

Looks vampiric and sickly

Obsessed with gold, in this case the Rang o' Powah

Has a true name (Smeagol) that he doesn't want others to know

Pretends to be friendly to gain others' trust

Always looks weak in public and pretends to be the victim as much as possible

Generalizes anyone that isn't him with derogatory terms ("tricksy false hobbitses")

Staged a false flag by making Samwise look as though he ate the bread

Acts in a manner so that friends become enemies by only revealing his true intentions in front of Sam to make his aggression seem unwarranted