It's not totally redundant. The index on last_name alone will be more efficient than (last_name, first_name) because the index will be able to contain more keys

It's not totally redundant. The index on last_name alone will be more efficient than (last_name, first_name) because the index will be able to contain more keys per index page. The difference can be significant if you're doing something that does an index scan on this column.