It would be perhaps confusing to have a category list that was sorted by something other than ascending/descending order for that category.
That depends on how the user's mind works. I prefer to stick with 'first name - last name', as that's how most artists (music and video) are known. Nevertheless, some are used to names being sorted by surname, and it takes some effort to look for 'John Coltrane' under 'J' rather than 'C'.
If you have a field with individual artists in 'last name, first name' format, that field can be used as a sort preset, and the preset used as the sort setting for the [Artist] category in a view. 'John Coltrane' is then sorted as 'Coltrane, John'. The sort field, of course, must also include non-individual artists (as [Artist]) in order that it can be used as a sort key for all artists.
To create a sort preset, use a
Group by or
Sort by menu on the tab menu of a view in Standard View. Use the 'Custom' item at the end of the menu to set (what I call) [Artist.Surname] as the sort field, and then select 'Preset' to give that a name (I named mine 'Artist.Surname'). Then that preset will appear in the list of sort options available in the Category dialog of the Theatre View configuration (shown in screenshot).