A sobriquet is a nickname, sometimes assumed, but often given by another.

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Distinct from a pseudonym that is assumed as a disguise, it more resembles a nickname and usually is a familiar name, familiar enough such that it may be used in place of a real name without the need of explanation. This salient characteristic is of sufficient familiarity that the sobriquet may become more familiar than the original name.

An example is "Honest Abe" for Abraham Lincoln.

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More Info: www.wikipedia.org