I should think they're simply called 'innkeepers'.
A landlord is the modern equivalent of a male who owns an inn or boarding house.The female modern equivalent is landlady.In the past, a person who owned an inn was called an innkeeper. In some places, especially small villages in England, they are still called this.
The Inn Keeper - 2010 was released on: USA: December 2010
A person who owns/runs an inn or hotel.
A pubkeeper in England is called a "Publican" or "Landlord" and more often today the "Licsensee"
an inn keeper
Jeremy Bowen
Innkeeper
He was the keeper of the Sprouter Inn
Wirt ...from Wirtshaus....an Inn Keeper.
The cast of One Night at the Inn - 2010 includes: Felix Bell as The Stranger David Sterne as Inn Keeper
a park keeper