In some cases, the name Pomellina can also be a direct derivation of the word pomella, which means "apple" in some Italian dialects. In other Italian dialects, the same word means "grapefruit", as a variation on pomello, which is the usual word for the fruit. And finally, in the Venetian language (which is often mistakenly believed to be an Italian dialect), the word pomella means "red berry (of thorny bushes)".
As you can see, all etymological explanations for the name ultimately refer to some type of fruit. As such, we can conclude that the aforementioned Latin pomus and/or pomum are ultimately at the very root of each of the explanations, because Italian (as do its dialects) and Venetian are ultimately descended from the Latin language.
The name Pomellina was mainly used in the Republic of Genoa during the Late Middle Ages. A known bearer of this name was Pomellina Fregoso (c. 1387-1468), a Genovese noblewoman who was the wife of Jean I of Monaco (c. 1382-1454), who himself was ultimately of Genovese descent as well. Her name was gallicized to Pomelline in Monaco, as it was (and still is) predominantly a French-speaking country.