Let's say Noble House A begat a cadet branch Noble House B, but Noble House A became extinct in the male line, such that the cadet branch became the most senior branch. Would Noble House B ceased to be known by its cadet name and revoke to the title of Noble House A.
I agree with CaptainShadow, but with a slight proviso:If the Valois and the Bourbons are anything to go by, Noble House B will still be known as Noble House B.
If the houses are distinguished by having locations appended to their names then when the main branch died out, the cadet branch could just stop using the location identifier, such that it appeared to be a continuation.
Here's what I mean:
Noble House A ('Nobbs') begets Noble House B ('Nobbs of Smallplace'). Noble House A is normally just referred to as 'Nobbs' though sometimes as 'Nobbs of Bigplace' where a risk of confusion exists. Noble House B is always referred to with the location identifier: 'Nobbs of Smallplace.'
Noble House A (Nobbs (of Bigplace)) dies out.
Noble House B (Nobbs of Smallplace) is now the only bearer of the name (Nobbs) so the location is normally dropped: 'Nobbs' now refers to Noble House B.
Where there are lots and lots of different names, this is less likely; it'll happen more when multiple families are descended from one 'original' family. (For example: MacDonald of Glencoe vs MacDonald of Glengarry, both members of Clan Donald). Once you get into the age of emigration, you might find families where the main family is in one country and the cadet branch in another, so both are just referred to by their name, without location, except in formal circumstances (for example the Swintons of Kimmerghame, in the Scottish borders, are a cadet branch of the Swintons, with the chief branch (Swinton of that ilk - meaning Swinton of Swinton) now living in Canada, I think).
Sorry, that was longer than I thought it would be when I started typing!