Sorry, Clare, I cannot help with an ID, but this looks very much like the variety I saw in the northern part of Vietnam (See
Vietnam Bananas). Since it is prevalent in, - possibly even limited to - the north, we may assume, that it tolerates cooler temperatures. While we still lingered in the south of the country, the temperatures in some parts of the north dropped for a few days down to freezing overnight. If you have plenty pups, it would be interesting to experiment with minimal protection next winter.
Unfortunately you do not display your local hardiness zone or which part of (California?) you live in. Therefore my suggestion may be inapplicable.
Best,
Olaf