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Re the Polhill Arms TQ5060 : The 'Polhill Arms', near Halstead, Kent and TQ5060 : Polhill Arms

Polhill is the name by which the incline by which the M25 climbs over the North Downs between Junctions 5 and 4 is officially known (TQ5060 : View From The Bridle Path Bridge). The tunnel by which the London - Sevenoaks railway cuts through the same stretch of the North Downs (almost directly beneath the pub) is known as Polhill Tunnel, and nearby is Polhill Bank Nature Reserve (TQ5060 : Polhill Bank Nature Reserve sign).

The obvious conclusion is that the name Polhill is because it is a hill - a corruption of Pole Hill, say.

But this pub suggests otherwise - being an "Arms" it implies that Polhill is a family name, and it turns out that the Polhills were a well known Kent family, one branch of which lived in nearby Shoreham, although the family could well have had Cornish origins (see http://polhill.info/).

So might it simply be that the use of the name Polhill to describe this location (which incidentally is not named as such on OS maps) derives purely from the pub, and the fact that it is at the top of a hill is coincidence?