According to Instagram, “When someone mentions you in their story, you receive a notification in your Direct message thread with that person — now, you’ll see an option to add that content to your own story. Tap it to see that story as a sticker – you can scale, rotate and position it and add creative tools like text or stickers on to it as well. When your followers see your story, the original poster’s username will appear and will be tappable, so people can explore your friend’s profile as well.”
However as Instagram notes, this is only applicable to those who have public accounts. This means that if your friend has a private account and they mention you, obviously you won’t be able to share their Story because it is private. However other than that, you’re good to go! Instagram has been rolling out quite a few changes and new features to Stories, such as allowing users to reshare posts to Stories which we guess is Instagram’s take on the “regram” feature.