was a very popular given name in the 19th
century in honour of Arthur Wellesley, the first Duke of Wellington.
The surname is thought to be derived from the three places in England with that name, one being a large town in the south-west, in Somerset. The meaning seems to be "The settlement of the Weolingas", which was an Old English tribe.
The Duke's family name, Wellesley, was from a small village in Somerset. The name Wellington was chosen, apparently, because it was similar to the family surname and the town of Wellington was the nearest large place to their original home before the family moved to Ireland. Arthur had been brought up in Ireland.