An item's short name is displayed when the item is acquired as a "Rare (one-time) Reward" or from the Dabo Wheel.
Often times items are sorted in-game by their short name rather than their full name (also by whether the item is a 1-time reward and by rarity).
Short name of crew members is called Character name. All crew members with the same short name are versions of each other. (Versions are most relevant in events). Note however that not all versions share the same short name–for example, Changeling Bashir is a version of Changeling, not Bashir. List of crew short (character) names.