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As answered in the comments, it looks like this feature has a few names:

• Just an "eave", like any other eave on the house
• "eave return", or "full eave return"
• "cornice return" or "full cornice return"
• "closed gable"
• The whole gable end makes up a "triangular pediment", of which the circled section is a horizontal cornice

There are a handful of colloquial terms for specific types of "eave returns" - "pork chop returns", "mutton chop returns", "bird boxes", "catwalks".

Sources:

• http://www.ontarioarchitecture.com/cornicer.html
• http://www.contractortalk.com/f14/what-type-eave-called-see-picture-38794/
• https://www.houzz.com/discussions/2287882/why-are-full-cornice-returns-aka-mutton-chops-disliked-here
• https://www.britannica.com/technology/pediment-architecture