That's just naming convention, both at the time and in historiography. Robert Stewart is known as Lord Castlereagh, Lord Liverpool's actual name is Robert Jenkinson, Wellington's elder brother is called 'Mornington' a great deal.

The reason for this is pretty simple; there can be quite a lot of Stewarts, Cannings, Wllesleys and Jenkinsons, but having multiple peers titled to the same location is quite rare, so it's far simpler to refer to someone as 'Wellington' rather than 'Wellesley', as you could be referring to Henry, Arthur or Richard, all three of which were involved in British politics.

Hope this answers your question!