If you know that this is specific List<T>and not another type of collection, you can use List<T>.ConvertAll:
Converts the elements in the current List<T>to another type and returns a list containing the converted elements.
Example:
List<string> myObjectNames = myObjectList.ConvertAll(x => x.Name);
, , , LINQ Enumerable<T>.Select Enumerable<T>.ToList:
List<string> myObjectNames = myObjects.Select(x => x.Name).ToList();