On my first playthrough I called my PC Joseph, and it turned out that the first 'just' master of the Hotel was an early Christian called Joseph, who helped set the the path away from the torture chamber Labyrinth to the Hotel as it stands.
At first I thought this random coincidence was part of the game, and whatever player name you chose ended up being that guy's name, creating historical symmetry if you chose the kind path, or irony if you chose the Ruthless path. Some of the reforms you can make during the game seem to be as significant as the original changes made by Joseph 1st.
Obviously this didn't pay off at all during the game and I realised there was no way the devs would change the backstory to include whatever random name the player chose i.e 'Nooblord7000', but I thought it might be interesting as an Easter egg if there are certain names Asterion reacts to during the opening chapter of the game after he meets the player.
We are told that he knows the name of the new master as soon as the PC takes the deed to the hotel because this is part of the magic of the contract, so perhaps he would have had some time to stew over it. It's not clear how much about the master Asterion knows other than the name though.
Some like Joseph could have a positive or curious reaction given the history of the name, and others that belonged to less kind masters could elicit an initial concerned reaction, for example Clément. Asterion did say he worried that one of Clément's relatives would take over the hotel. I wouldn't see the need to react to silly names other than maybe in the speedrunner playthrough?
It doesn't need to impact the game beyond a small Easter egg IMO as the PC seems free (so far) to choose his own actions according to the whim of the player so whether his name has meaning becomes irrelevant as soon as he shows his real colours.