Sort on last name, first name, or both?

Definitely have a column for each part. That gives you much more flexibility. So you could sort by surname, but print "firstname surname", for example.

If you don't have the screen real estate to have a column for each part, you can combine them into a single string whose format represents the sorting order. Each click on the column header cycles to the next sort order. For example:

Default: sort by last, first (ASC)

Bimbleman, Wally P.
Zonkenstein, Arnold Q.

1st click: sort by last, first (DESC)

Zonkenstein, Arnold Q.
Bimbleman, Wally P.

2nd click: sort by first, middle, last (ASC)

Arnold Q. Zonkenstein
Wally P. Bimbleman

3rd click: sort by first, middle, last (DESC)

Wally P. Bimbleman
Arnold Q. Zonkenstein

etc...

Easier to read an entire name this way (vs. having it span across columns), takes up less screen real estate, and frees you from having to decide upon a single format & sort.