Since 2019, Array.prototype.flatMap is good option.
options.flatMap(o => o.assigned ? [o.name] : []);
From the MDN page linked above:
flatMap
can be used as a way to add and remove items (modify the number of items) during a map. In other words, it allows you to map many items to many items (by handling each input item separately), rather than always one-to-one. In this sense, it works like the opposite of filter. Simply return a 1-element array to keep the item, a multiple-element array to add items, or a 0-element array to remove the item.