I have always referred to the pub between Kirkby Lonsdale and Cowan Bridge as the Woop Hall, but when I mentioned it to someone at work, she said it's the Hoop Hall. Whoops.
So what is it?

Both right / wrong 
https://www.whoophall.co.uk/

According to Longman?s Pronunciation Dictionary, the silent-w variants of whoop are more common in American English, whereas the w is typically not silent in British English. An interesting exception appears to be that of whooping cough (a rather serious medical condition explained here, not something to whoop about), which is predominantly pronounced without the w in both American and British English according to the Longman Pronunciation Dictionary.

https://painfulenglish.com/2019/06/09/how-to-pronounce-whoop/

Oxford say "woop"  https://www.lexico.com/definition/whoop

but Cambridge seem to pronounce it "rook" - on my sound system, anyway!  https://dictionary.cambridge.org/pronunciation/english/whoop

Whatpub.com says "hoop" for the hall  https://whatpub.com/pubs/LUN/213/whoop-hall-burrow

Oh well...

It's a silent w to us locals 

"Goin darn oop all f pint an kishe" as they say in Kirkby.

As fjell says, in broad Yorkshire it'll be a silent w & h (and another h on the 'all).