Here are the steps to name a segment and make it retrievable:
Click the Star > type the name you want > Save Audience > you will see the segment under Segment Shortcuts
So what happens when you add or remove a filter, or change the geography?
If you want to make changes to the saved segment, select the changes, then you will have to re-star, as the Faraday system will save the original segment.
If you want to save your new work, star the segment again -- then you'll have the original as well as the latest changes.
You can remove starred segment by opening it up, and hitting the star again. This will permanently take it out of your Segment Shortcuts list.