Named after...
The Midnight Inn received thousands of new guests every day, at the very least. Although most of them arrived at the Inn through the use of golden keys, enough of them came from golden doors that opened randomly for Lex to have realized that the occurrence of those doors was not truly random. Although he had yet to figure out the pattern with which they opened, he could determine that they were more likely to open up in areas where they were likely to be discovered.
There was a part of him that suspected there was even more to it than that, as he had seen a few odd patterns in the kinds of guests that arrived through the golden doors. Suffice to say, they were more likely to be interesting or significant characters as compared to those that arrived through the spread of golden keys.