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) "On the recommendation of the assistant city surveyor, the committee approved of a proposal of Ballysillan Holdings Co Limited to name a new street on their property situated off Crumlin Rd, Squires Hill Rd". (5th March 1963).
Further Information
Nelson McCausland blog https://ballysillan.blogspot.com/2014/04/ballysillan-street-names-and-place.html