This story about edge names will become much more interesting if we start working with multigraphs and remove edges at the same time. Consider the following graph:
Distinguishing the two edges between 1 and 3 is important because removing one merges the green/orange, removing the other merges the blue/orange faces. Currently, we can only distinguish edges by index. If we repeatedly do such removals (face mergers), the edge indices will change. Thus the only reliable way to refer to edges consistently is to give them names. Then it follows that fast lookup by name might be a good idea.
Another application is moving between the original graph and its line graph.
I think we’re not quite there yet though, it’s not yet time to implement fast edge lookup by name. We need a more practical use case first.