You will probably get better responses soon, for now I can tell you with confidence that it is a dracaena...but there are many different kinds and I don't know them well enough. I'm pretty sure they can handle heavy pruning, but I would wait to see what others have to say.

You have a beautiful Dracaena, I'm sure others will give you alot of advice, I think you can air layer it, but I cant be of any more help

Dracaena marginata. I would cut the tall part somewhere around the red line, so the shorter part will help hide it until it grows a new top. The blue line is where I'd remove the extraneous trunk to propagate the top of the tall part, but that's purely a matter of opinion. The remaining trunk between the lines is also likely to propagate. The easiest thing to do if you don't want multiple pots of this same plant are to stick them in the "dirt" with the mama. Pretty vague instructions, so please ask if you need more info.

After you cut, you may notice the plant is using water less quickly, so be ready to water a little less often than you have been if that does prove to be the case with your plant.

This discussion is about a rubber tree, Ficus elastica, but the pruning/propagation principles are the same, if you'd like more reading material and more pics.

This is very helpful! Thanks. I wish to propagate trunk and top in same pot. How deep should they be placed?

I would stick them in until I hit bottom. You've got plenty of material there, that would devote the entire submerged length to possible roots. Below is a propagated tip, (differently striped leaves, but same plant,) after being unpotted. Dracaenas can make extensive root systems. For the "naked" piece of trunk, just be sure it's in the same direction in which it was growing.

In the future, you could rotate the plant more often to keep it from leaning toward the light but I don't blame you for letting it lean the way it is in the pic. I bet it's really cool to walk under your tree, and it certainly has space to sprawl there, and seems to fit really well, pretty cool.

...and good luck with your move! The timing of this could be somewhat tricky. How are you moving this plant? It might be best to do this as "last minute" as possible, so in case there's any shifting, there won't be tiny new roots being damaged. Tough call though, I'm sure. What shouldn't be done last minute when moving, right?

if it was me i actually wouldnt cut it. that trunk is beautiful

Teen, unless you have a ceiling stretcher to loan Beachcomber, this plant won't fit in her new house. Please read the post.

What purpleinopp said is pretty much spot on. Once the cut stem has some decent sized heads you can repeat the process with the shorter one.

Hi
This has my vote as the worlds hardiest plant Most of mine are landscape plants but two of the fancier hybrids are in pots. One is growing on a slab of granite with no pot at all..
You can cut them anywhere at any time but I warn you that the cut trunk will sprout in several places The cutting will continue upright . have never had one fail to sprout in any kind of soil or even water
When I pruned one of the landscape ones had about 25 stems laying on the ground . Hurricane struck dropping a shadehouse on top along with several tree limbs Took almost 12 weeks to get the debris removed . Every limb had not only sproutrd had grown roost into the ground!!
Might add they were also under around 3 feet of water for over two weeks!! Is that hardy or what?? lol

Hi
This has my vote as the worlds hardiest plant Most of mine are landscape plants but two of the fancier hybrids are in pots. One is growing on a slab of granite with no pot at all..
You can cut them anywhere at any time but I warn you that the cut trunk will sprout in several places The cutting will continue upright . have never had one fail to sprout in any kind of soil or even water
When I pruned one of the landscape ones had about 25 stems laying on the ground . Hurricane struck dropping a shadehouse on top along with several tree limbs Took almost 12 weeks to get the debris removed . Every limb had not only sproutrd had grown roost into the ground!!
Might add they were also under around 3 feet of water for over two weeks!! Is that hardy or what?? lol

Thanks for all the tips. Attached photo of cut and propagated plants. Will try to update again in a few months to let you know how it is doing.

Cool, that's exactly what it would look like if I had done it, so great job!