Thanks to everyone that replied, I now know why it was named.

But I am still confused about where the person who donated the land lived.

Quine's Hill 1823 on land donated by John Quine of Ballig ( Ballalig, Ballaslig ?)

I found a Ballig (Onchan) plus Ballalig, Ballaslig.

Does anyone know which location the donor was from?.

Probable donor
John Quine (married 01 Mar 1808) Catherine Bridson in Santan with their son Edward continuing the farming at Ballig.

Also does anyone know his parents?, If it was the Ballig Quine's my information ends at this generation:

Edmund Quine b: 1730 Braddan
married 4 NOV 1766 Kirk Braddan Elizabeth Lewin LEWN b 17 APR 1739 Ballig
Children
Elizabeth b:03 Aug 1767 Ballig, Braddan,
Edmund b:10 Mar 1769 Ballig, Braddan,
William b:18 Mar 1771 Ballig, Braddan,
Alice b: 10 Aug 1775 Braddan,
Catherine b:01 Apr 1778 Braddan,
Eleanor b: 1781 Braddan,
Alice b: 24 May 1784 Braddan,
Isabel b: 24 May 1784 Braddan,
Mary b:25 Jan 1773 Ballig, Onchan, married John Quine and died at Arderry