Only you can dash in place without dashattacking... which would be ledgedashing. When you choose to do a dashattack, you're ledgedashattacking.That sounds too clunky. Besides, you ARE dashing at the edge. The dash attack is just a bonus, making dashing at the edge useful in a way.
If Ledgedashattacking is too "clunky", then there's LDA:ing, as Thiocyanide suggested.
Ledgedashing = Dashing in place at the ledge
Ledgedashattacking = Dashattacking in place at the ledge