Jonathan Rosen, one of the architects of New York City Mayor Bill de Blasio’s 2013 campaign, wears many hats: political adviser to the mayor, a consultant to a nonprofit that advanced the mayor’s agenda and head of a public-relations firm that represents clients with city business.

This week, as Mr. de Blasio defended his administration’s decision not to release Mr. Rosen’s emails under New York state’s freedom-of-information law, Mr. de Blasio gave him a new title—agent of the city.

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