Interesting case of double-layered false nominative determinism. Although foresta in Italian means "forest" and thus the surname would seem eminently plant-based, it actually means "foreigner", which I guess he also ended up being as Italian immigrant in the US. The etymology of forest and foreigner is closely related and means basically just "(from the) outside".
In Portuguese "forasteiro" can also be used to mean "foreigner" or "outsider".
Wow, that's a really sneaky "false friend" in Italian! Especially since it even has the meaning of "forest-related" in other Latinic languages, e.g. in French route forestière = forest road.