Your trail name is your nickname that you are called by on the trail because of some feature or action of note for which you are known. While some people give themselves their own trail name, that is generally not how it works as a trail name should be bestowed upon you by fellow hikers!
Example: A young woman was thru-hiking the Appalachian Trail with a gun that her father forced her to take for self protection. At some point she dropped it on the trail and a thru-hiker behind her found it and knowing whom it belonged to, caught up to her and gave it back to her. From that day on that hiker’s trail name was Gun Runner!