This Fuchsia has been grown as a standard. Almost any cultivar can be grown like this. It is a cultivation style, not a variety. Yours could be 'Lena' but there are 1000s of cultivars, so don't quote me. You can overwinter it but do not cut the main stem back. You need to keep that central stem as a permanent framework. Fuchsias do not do well indoors as there is insufficient light. I would put it outside as long as possible. Then you can overwinter it dormant in a cool basement or shed. You might have fun taking cuttings and growing your own standards.

Here is a link that might be useful: Growing standard fuchsias

Thanks for the reply! I haven't checked back in ages, I missed it till now!

I do not have a cool anything to overwinter plants, sadly - but I successfully winter my potted citrus indoors with a fluorescent grow setup and a south facing window. If I can keep those happy, I imagine I can keep a fuchsia alive, at least. I do not plan to cut back the main trunk, just the branches to make it a bit more even and compact to take up a bit less counter space. I do think I will try some cuttings, because I LOVE fuchsia and would love to have a taller one!

Thanks for your reply, I am sorry I did not see it until now!