A named professorship is not an academic designation, although recipients of named professorships would be individuals of high accomplishment. The primary purpose in naming a professorship is to attract and retain top quality faculty. A position can be named only when there is a source of funds sufficient to name the position in accordance with the University policy on naming opportunities.
Faculty of the rank of assistant, associate or full professor can hold a named professorship. For more details, see http://www.purdue.edu/policies/human-resources/vic1.html.