An allusion is a figure of speech that makes a reference to, or representation of, people, places, events, literary work, myths, or works of art, either directly or by implication. M. H. Abrams defined allusion as "a brief reference, explicit or indirect, to a person, place or event, or to another literary work or passage".[1] It is left to the reader or hearer to make the connection (Fowler); where the connection is detailed in depth by the author, it is preferable to call it "a reference".

In a freer informal definition, allusion is a passing or casual reference, an incidental mention of something, either directly or by implication: In the stock market he met his Waterloo.
A sobriquet

Sobriquet

A sobriquet is a nickname, sometimes assumed, but often given by another. It is usually a familiar name, distinct from a pseudonym assumed as a disguise, but a nickname which is familiar enough such that it can be used in place of a real name without the need of explanation...

 is an allusion: by metonymy

Metonymy

Metonymy is a figure of speech used in rhetoric in which a thing or concept is not called by its own name, but by the name of something intimately associated with that thing or concept...

 one aspect of a person or other referent is selected to identify it, and it is this shared aspect that makes an allusion evocative.