What is single word in English for a fake/false image (in terms of personality, not in terms of photograph) of someone?
Facade ("A deceptive outward appearance") may suit. Also consider disguise, persona ("a role or character adopted by an author or an actor"), and masquerade ("Acting or living under false pretenses; concealment of something by a false or unreal show; pretentious show; disguise"). Trumpery ("worthless finery; bric-a-brac or junk") may be used in achieving a false image; by analogy one might call a false personality trumpery. Spelling note: Be careful not to leave out the er before y.
You may also find useful words (such as two-faced, Janus-like, deceiver, fake, double-dealer, duplicitous, polymorph, chameleon, wolf in sheep's clothing, poser, duplicitous, back-stabber, hypocrite, fraud, imposter, poseur, whited sepulcher, Devil in disguise, fool's gold, mirage, simulacrum, et al) in answers to the following questions:
• #24216: "I'm in need of a word that describes someone who has two personalities (they don't necessarily contrast each other, good/evil)."
• #72916 "What word best describes a person who is deceitful and very complicated to understand? As they say, he wears several masks."
• #42404 "A character in the movie is really bad, but when she talks with others, she pretends to be an innocent/ good woman. I want to know how to describe this kind of person."
• #71398 "What are common phrases that describe something that appears good but is actually bad?"