In the old days (meaning pre-Tudor times) the land of Britain was divided into parts each assigned to a man bound to the king by oaths of fealty and often blood ties in one way or another. Such men were responsible for supplying the king with soldiers, if need be, and themselves serving as knights. These men were generally known by the name of the land to which they were assigned. So, for example, Ralph Neville was created Earl of Westmorland by Richard II in 1397. Since this fiefdom was the greatest of all his possessions at the time, he would be known as "Westmorland" in certain contexts, especially military ones.
There are an important reasons for this involving honor and respect. For example, let's imagine I am speaking to the king about Neville's possible participation in a war, I will not call him "Robert Neville", because that would imply I know him, to use his name in a familiar way. I might be construed as implying I were his friend, and even if I were his friend, it would be rude of me to throw his personal name out in front of the king and others. This might get back to him, people saying "Durden was calling you Neville to the king". If I were not his close friend, he might be very insulted by this. It is like those low people and magazines nowadays who refer to Hollywood celebrities by their first names, as though they were somehow their friends.
To show proper respect to such people I would refer to them by their fief or by their title.
Later on, such people became private persons, but the same customs of nomenclature and respect continued, so that titled people would even refer to themselves by their baronage, no matter how small it was, as to suggest their importance.
Now, of course, such usages are quite conceited, because even Ralph Neville, a real peer, would always sign his personal name "Ralph Neville" to any document or letter. In other words, other people would refer to him as Westmorland, but he himself would use his own name. So, when someone like John Forrest starts signing his name as "Forrest" he is putting on airs as though he is some great man, without really understanding the custom in the first place.
I should probably point out that there is point of legality that is significant here. At a certain point the British parliament made laws respecting the use of one's name, and a special exception was created for peers (meaning a member of the House of Lords) whereby they could legally sign their name by the name of their estate, thus "Marlborough" or "Norfolk" or whatever. Over the years, some people considered it significant whether you had the "legal" right to sign your name in this fashion. In general, it was the custom only for those with inherited titles from landed estates to use the title itself. Those, like Forrest, who received their lordship from a civil source would use their surname. For example, Frederick Stanley was known as "Lord Stanley", not "Lord Derby".