In Arcadia, why are the children of Lord and Lady Croom (in both time-periods) named Coverly, and not Croom?
In England, titles often do not mean that you have to change your last name. The position of the Earl of Croom meant that you retained your name and were referred to as Lord and Lady Croom whilst keeping your surname. This is why Augustus, Thomasina and the modern day children of the Crooms all have the last name of Coverly, the name of their parents. Note how this is referenced in the text:
A letter, we have seen, written by the author of Headlong Hall nearly thirty years ago, tells of a visit to the Earl of Croom's estate, Sidley Park--
The "Earl of Croom" is a title that was given or created for a certain person and did not change their name. In England, it is perfectly possible to have a title and for this not to affect the last name you have. Note the way that the Royal Family of Britain have a last name--Windsor--that they retain in spite of the many titles and positions that they have, such as the Duke of Cambridge, for example. The Crooms are known as the Crooms because of their title, but their last name is Coverly, and this remains true for the modern-day Crooms.