Question for Italian wine experts - Montepulciano

We drink a lot of Montepulciano d'Abruzzo, and I was idly wondering:

What does Montepulciano mean - if anything?

Was the grape named after the city of Montepulciano - where they don't AFAIK grow the grape Montepulciano?

Hi Peter,
I’m no Italian wine expert, but Montepulciano might mean “public hill” or “hill for the people”

Salute