I'm not sure what the name of this hornpipe refers to. I far too young to remember ha'pennies. The "Poll" sometimes manifests itself as a "Paul". That makes things even less clear to me.
In Bill Ochs’s handbook for tinwhistle he advises that the piece began life as “Molly Macalpine” and shifted from being a courtly piece to being a hornpipe. As it descended the social ladder, so to speak, Molly became Polly and Macalpine became “halpin” then “Ha’penny” and thus to the hornpipe we play today.
He adds that the Molly Macalpine piece was published in 1796 - Edward Bunting’s “General collection of the ancient Irish music.”