As a middle name, this is very likely to be a use of the surname Boar rather than a direct use of the word "boar". According to A Dictionary of English Surnames
by Reaney & Wilson
, Boar is an English surname, going back to the Old English word which yields the modern word "boar". It probably was originally a nickname for someone whose neighbors thought he looked like or acted like a boar.
Perhaps you should look into records from East Sussex in the 1860s to find if there were any families with the surname Boar living there when your great-great-uncle was born.