It looks like a swan/goose gourd. If it were growing on the ground, the neck would likely be bent, creating the head and bill of a swan or goose.
But, no matter what it is, it will make a great birdhouse.

Jan

Thank you Jan! : )

Looks exactly like my "swan gourds". I never thought about it and grew them in a cage and the necks are all straight.
Tom

Yes, that looks like a swan gourd. To answer your other question, yes again, you can leave them hanging if you'd like. They won't fall off, those vines and stems are very tough. If you do cut them off, make sure you leave at least half of the stem attached to the gourd, don't try and break it off at the place it's attached. Leaving some stem will allow them to dry properly, and you can remove it once the gourd is fully dry. Takes lots of patience.....