Also known as Prentjiesberg in Afrikaans this literally means 'small pictures mountian', derived from the San paintings found in the area.'Appryntjie' which is an historical word for a freed slave or a cheeky insolent person or a person of mixed blood, could also be referring to these San People! The Xhosa name for the mountian is 'UMngqazo'.
References
New Dictionary of South African Place Names by Peter E Raper