'peloso' means 'furry.' 'Pelosi' should be same same.
LOL! I speak Italian, but never gave it a thought -- "pelosi" is the plural of "hairy" or "furry." As a family name, it must have originated with a medieval family who became known as the Furries or the Hairies. This is roughly equivalent to English medieval names such as Farmer, Miller, Barber, Cooper (barrelmaker), Chandler (candlemaker), etc., that were about a person's livelihood -- "go see Gareth the Farmer" soon became "Gareth Farmer."
In the case of Pelosi, it could have been about someone's physical appearance, but more likely it was an identifier of a medieval family guild of fur trappers, fur traders or tanners of fur leather.
PS:
If the name means "fur trapper", etc., where is PETA on this?