The usual way of noting who visited a country house is to look at diaries.

Many people during this period kept journals of their travels,and recorded their visits.

For example , the 3 volumes of the diaries of the Hon. John Byng, who toured england between 1781-94 are chock full of references ( some very uncomplimentary) to the houses he visited( or in some cases failed so to do,because he was not admitted!)

We know that Horace Walpole at Strwaberry Hill,Twickenham,kept records of all his visitors.If you recall from a previous post, I told you that he asked his visitors to apply in writing for admission tickets. From 1784-97 there were an average of 300 people a year viewing the house.

One dairy which does help us is that of Mrs Lybbe Powys( a distant connection of Jane Austen's: her cousin Edward Cooper married Mrs Lybbe Powys' daughter).

She writes in 1776;

"...few people pass by Wilton( home of the Earls of Pembroke-JW) ,as in the porter's lodge, where he desired us to set down our names and the number of our company,we saw by the book there had been to see it the last year,2,324 persons ..."

So if Mr Darcy's staff kept a record,Elizabeths Bennet's name would certily have been entered into a book.Unless Mr Gardiner signed on behlaf of them all( and then Darcy would have no idea -as I think I am corrct in stating that at this time, though he ws aware that Elizabeth had relations who lived in Cheapside, he had no idea of their surname).

It also depende on Darcy seeing the record.It might be shown to the houeskeeper and the steward,but unless Darcy was a very assiduous master of his household I ca'nt really thinnk that he would be botehred with the details.He might be told the number of visitors per year,but giving detials of the names might be too much.