Healbot does have an alphabetical listing, which is what you'd want ideally.
Not sure how to do it, but it has been answered in several Healbot threads.

Alphabetical or a fixed order is a requirement for repeater regions.
You will definitely want every toon to be listed, and to not use the "don't list current toon" option.
Otherwise, you won't be able to heal that toon via repeater regions.