@ladyofautumn Thank you for bringing up an interesting topic!

Larger English houses are not always called mansions; the usual term is 'stately home'. Whether they are always named is beyond my knowledge, but I'm sure a named property (like Pemberley in Jane Austen) could have its name changed by a later owner. 
I think the simple answer is that C.S.Lewis didn't give the Professor's house a name!  It is just referred to as 'the Professor's house'. The houses where Polly and Digory lived in London were just nice terraced houses of probably three storeys plus a basement, and referred to by the owners or occupants.  (terraced houses are joined in a row, as you have read in The Magician's Nephew).

At the end of The Last Battle the Pevensies actually see the Professor’s house from the new Narnia.  Apparently it still existed since nothing good there is ever lost or destroyed.  It was considered a unique home and people came from miles away to tour it.  It makes you wonder if as an historic home it would always have been preserved. At least that is way that places like that are regarded here in America, and I think it would be the same in England. Often historic homes are restored to look like they did decades or hundreds of years ago. Why wouldn’t it be the same with the Professor’s house? 

I think the logical answer is that, as @coracle says, Lewis simply didn't give the house a name. In real life — if it existed in real life — it would certainly have had one. Stately homes in Britain always do, as far as I've ever seen, regardless of who built or owned them in the first place. (I've lived in the UK for 12 years now and have a National Trust membership, so I've visited a lot of historic houses!)

But as the name of the Professor's house isn't important to the story at any point, it simply isn't referred to. Giving it a name might then raise questions of where abouts it is in England and who built it and what its history is, none of which is important to the story either. I get the impression Lewis didn't want to distract his young readers with invented details like that, but just to keep the focus on the plot — on what happens there once the four children are staying there. Everything else about the house is entirely up to our imagination!

Lewis himself owned an estate named The Kilns. He was doing well, but I don't think he was what we would call wealthy. In England, it seems, even modest country houses can get names. It doesn't matter if they were built by nobility or not.

In Dawn Treader, wasn't it mentioned that the Professor had to sell the house? That wasn't explained.

As for the house later being destroyed, that wasn't explained either, but since it was old, fire was the most likely culprit.

@cobalt-jade The Kilns wasn't a Stately Home, but a small-medium sized house with some land. His friend's mother and sister lived there, as well as the two Lewis brothers. They added an extension to make enough space.

Lewis gave a lot to charity, but he only had a university lecturer salary. 

I never got the impression that the professor's house was a Stately Home. Most stately homes (the likes of Chatsworth House etc) are absolutely massive, like the size of palaces, and as you say, would probably be on a named estate, with hundreds of staff, and be owned by a member of the nobility.

However large mansion houses of the size described in LWW are much much more common. My village is a pretty average and anonymous village of zero noteworthiness in England, ... And yet it still has 4 big manor houses. Not just big houses, but houses with big estates too. They aren't named, were never owned by Lords or Dukes, but they are still sizeable things (just not on the scale of a Stately Home).

It's also worth noting that in the early to mid 20th century (around about the time that Lewis was writing LWW) many of these large country houses were falling into disrepair, and for various social and economic reasons were even burned down by their owners who could no longer afford them... Wikipedia says around 1200 houses in England were destroyed during this period, and one documentary I watched on it said it was hundreds a year being destroyed at one point.

Many house owners at this time did turn towards house tours as a means to help pay for the upkeep, and for a while, particularly in post-war Britain where people were keen to experience a slice of luxury,  it was quite popular for even in the smaller country houses to run tours... However once the big estates got in on the action, and the post-war middle class started to become more affluent, the smaller country houses couldn't compete... And burning them down for the insurance money was often the inevitable last resort.

I guess which is all a way of saying, that in 1950 when Lewis was writing, a large country house would not entirely have been seen as an extravagant luxury, but would perhaps even be considered as an inherited financial burden 

I think giving the professor's house a name might have actually made it less mysterious somehow. Maybe C. S. Lewis wanted it to be so that whenever kids were taken on a tour of an old house out in the country, they could imagine that it might be the house. 

Posted by: @col-klink

I think giving the professor's house a name might have actually made it less mysterious somehow. Maybe C. S. Lewis wanted it to be so that whenever kids were taken on a tour of an old house out in the country, they could imagine that it might be the house. 

Good thought — I reckon that's quite likely, and there's certainly evidence that that's how Lewis's own imagination worked and how he liked to encourage children to think. I can't remember exactly which book I read it in, but Douglas Gresham recalled that when he first met the man who was later to become his stepfather (and was disappointed to discover that the author of Narnia didn't wear a suit of armour and carry a sword), they were being shown into The Kilns when young Douglas noticed a big wardrobe and asked Lewis, "Is that the wardrobe?"

And Lewis simply smiled and responded: "It might be..."  

@cobalt-jade VDT says that somehow the Professor had become poor, and had moved into a cottage with only one spare bedroom. 

Posted by: @coracle

@cobalt-jade The Kilns wasn't a Stately Home, but a small-medium sized house with some land. His friend's mother and sister lived there, as well as the two Lewis brothers. 

And as far as I remember, his friend's mother was the owner of the Kilns, and the Lewis brothers only had a legal agreement that they had the right to live in the house for all of their lives.

I guess that Lewis wanted the place to be a bit anonymous and not a place anyone would try to locate, and therefore never mentioned a name for it.

@varna Lewis paid quite a bit too, but it was put in Mrs Moore's name, and yes, with lifetime residence for both brothers.

(After Warnie died, Jack's friend's sister sold it. In the late 1990s, an American trust bought and restored it. Postgraduate students can rent a room there, and they act as tour guides for groups of visitors. I went in 2019)

Is there any reference to the age of the Professor’s house?   I am assuming that it was built in the Victorian era, which is the approximate time setting of part of The Magician’s Nephew.  This would be about the time of Charles Dickens’ novels, although the house may have been even older than that.  At the time of The Lion, the Witch, and the Wardrobe the house was probably at least a hundred years old (or older), although I am not sure of the exact age. Was there any hint of when it was built in any of the books?  

Posted by: @narnian78

Is there any reference to the age of the Professor’s house?   I am assuming that it was built in the Victorian era, which is the approximate time setting of part of The Magician’s Nephew.

I assumed from the way C. S. Lewis described it that it was way older than that. (Of course, Queen Victoria's reign did last a very long time.) I got the impression that the house was old when Digory first moved in as a boy.

@col-klink 

There are houses in England that date back to the time of Shakespeare. But I am not sure if the Professor’s house is from that period.  I thought there were some references to things like suits of armor and other items of the Middle Ages in the house, but they may have just been eccentric things that the professor owned. There were many books, although books that people owned were less common in Shakespeare’s time since fewer of them were printed. It is possible that the house was built in the 1600’s or 1700’s, but the 1800’s does seem like a time old fashioned enough for the way it was described. The Professor who lived there in the 1940’s certainly had his own library. More people owned books in the nineteenth century, and it is very likely that the Professor kept all of them.