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It's the other way around: Psychology is a discipline within Cognitive Science, which includes Artificial Intelligence, Neuroscience, and possibly Philosophy of Mind. Research work in Psychology presumably makes you a Cognitive Scientist.
Arnon's answer is right, but I thought it might help to explain why. Cognitive Science is the study of minds. This can include human minds, other animal minds, and artificial minds. The method could be to study how agents with minds behave in experiments (psychology), to study the physiological properties of biological minds (neuroscience), to create and ...
You might be referring to mimicry or linguistic mimicry. Mimicry is more broad than just vocabulary and expressions, but the general principle of imitating what others in a social group are doing applies.
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