Fake means πλαστός, απομίμηση, ψεύτικος.
Fake Greek might translate to ψευτο-Έλληνας or απομίμηση Έλληνα.
This is not a commonly used expression. Maybe you can give me a complete sentence where you heard the "fake Greek", so I might better help you.
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Vasiliki Baskou, Instructor/Director, https://learn-greek-online.com.