Late to this conversation, just wanted to add a couple of thoughts, coming from the aloe world.
It is a pretty fabulous plant, appears to be doing well.
For what it's worth, it's growing in a really low light situation (for an aloe) and that may explain its stemmy, cascading behavior. The height of the pot and the distance from the window mean it probably doesn't "see" the sun much for most of the year.
It looks really unlike the version of Aloe juvenna that I have here and that I have seen elsewhere, which is characterized by tight rosettes with leaves stacked right on top of each other. My reference says stems of this plant may grow to about 18 inches long. But the low light may explain the differences in appearance. There are also hybrids of this species in cultivation, and many other aloes with a sprawling habit.
So I guess my conclusion would be that I couldn't really identify it with any certainty, but I have almost no experience with aloes growing indoors away from the rays of the sun. My suggestion would be to try taking a short cutting from the tip of one of the stems (maybe use this as an excuse to prune a stem that is becoming overly long to deal with) and plant that cutting in a new pot, right next to your sunniest window, low down at sill level. Then wait and see how it grows, what it looks like, etc.
Tips for this purpose if you choose to experiment:
This is best done in spring with the strong light and warmer temps of the season. Now is about the worst time.
Wait a week after taking any cutting to plant it. In the meantime remove any lower leaves that come off the stem easily after you cut. A gentle tug is sufficient, don't pull hard.
Plant the cutting with just the naked stem at the bottom buried. Use a relatively small pot. Use soil with good drainage (like 50% pumice or perlite) and a pot with holes at the bottom.
The cutting will turn brown while it is rootless and stressed, for example:
During this period you need to water with restraint. Once you see a little green creep back into the leaves, you can begin to water it like a rooted aloe.