After you have created a new segment, you have the option to edit or delete the segment. This will only work for segments you've created with your own data.
To find your created segments, hover over the Dashboard tab from any page on Strava and click My Segments from the drop-down menu. Then click to view the Created Segments tab.
Edit or Delete a Segment
Click on the segment in the list that you wish to edit. From the segment page, click on the Actions menu and select either Edit or Delete. You can move the slider above the map to edit the segment’s start and finish points. After choosing the new points and clicking 'Next,' you’ll be able to update the name of the segment or update the segment to be public instead of private. Keep in mind that you cannot make a public segment go back to private.