I should think they're simply called 'innkeepers'.
The Inn Keeper - 2010 was released on: USA: December 2010
A person who owns/runs an inn or hotel.
an inn keeper
I think it has to do with sounding modern & p.c. Inn keeper sounds a touch feudal; landlord or host is friendly and comtemporary. Same as saying bus driver instead of coachman. Personally I find the old terms more charming.
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
Could be a Park Keeper, or a Park Warden.
SpyGlass Inn
An inn is called an inn in Chaucer's Canterbury Tales. That is the medieval term for an inn. Similar words are tavern or roadhouse.
A person who is identified as a "restaurant keeper" in the 1900 US Census is a person who owns and operates a restaurant, just as an innkeeper is a person who owns and operates an inn (the forerunner of a hotel).