Squire's Hill is the name of an actual hill and also of a housing estate. It is possibly a reference to a 17th century lawyer Henry le Squire but it is much more probable that it is a reference to Sir Arthur Chichester who was the 'squire' of Belfast. (Nelson McCausland) The name Squires Hill Park off the Squires Hill Road was accepted by the Improvement Committee of Belfast Corporation on 8 October 1968. The proposal was made by Ballysillan Developments Ltd.
Further Information
Nelson McCausland blog https://ballysillan.blogspot.com/2014/04/ballysillan-street-names-and-place.html