Sorting is done by last name. Please note that even though HealthFrame lets you enter the provider name as you wish (first name first or last name first) it internally tries to assign the 'name parts'. Please see picture below and note what happens when I expand the name section, by clicking on the double down arrow.
So, if you enter Adams - John MD, HealthFrame thinks that the first name is Adams; the middle name(s) are - John and the last name is MD.
So the ascending sort order for the names you provided above would be:
Zoe Chris
Mary Cole
Smith David
Dr. Joe Martin
Adams - John MD
It may be better if you were to consider entering provider names in the "first name, middle name(s), last name" order. Then HealthFrame will interprete the name parts appropriately (you can check and modify if you ever feel it failed to interprete correctly) and alphabetical sorting should work.
Thanks,
Support Team