As much as you can customize any companion, at least.
If you’ve missed prior updates on the patch, you can also get a grip about the rewards included on the official site, you don’t need to go in blind. But the important takeaway is that the update is live and ready for you to enjoy, so jump on in and start exploring the dark side of the darkest planet. The whole thing is dark. That’s why it’s called “Umbara,” you see; Star Wars planets do not have subtle names.