What kind of plant is this and how do I cut it back to make it fuller?

It is a Dracena and they grow long and leggy trim off the brown tips--re-pot using a good potting soil and fertilize with Miracle Grow

Henriette is spot on

It can be cut near the soil and will sprout usually on 2 sides. Also the long stem that was cut off can be cut into 6 inch sections. Let ends dry. Mark top or bottom and stick into the soil with the downward end. In a few months they will sprout. It is a tough plant and multiplies easily !

It is Dracena Marginata one of the many caning varieties of house plants.Don't transplant! Keep it more root bound or it'll just grow more roots not on top- you can just use very sharp garden/pruning shears and cut it off,it will produce even more nodules. You can cut it off really short and it will form several new nodules & you can let them all grow for dense plant or if you cut it off towards top of plant,you will need to remove nodules/new shoots from top part of plant when you see them form so it does not get top heavy and break.Just use finger to rub them off as they form you can decide which ones to keep basically pruning to shape you want it to be. The top piece you cut off stick in soil at base of your plant and it will root or in water. Keep soil very dry then water thoroughly,they need good drainage and very bright light no sun.It looks really good.I think I'd leave it alone don't cut it back.Also if it is rootbound it will eventually grow new plant(s) thru soil it sends underground runners out.If it has 2 shoots I'd leave it alone sounds like it's already going to get thicker. Most house plants die from over watering & too much care. Just let it be, give it some water soluble Miracle Grow fertilizer when you water every 6 mos. you can use scissors & cut off brown tips if they really bother you just cut them off at sharp diagonal instead of blunt cut they will look much more graceful. if you get fungus gnats add Nematodes to soil, get them at Arbico organics theirs are guaranteed to be alive, they are beneficial organic pest control.

Cindy, I found you a couple of articles on trimming and care for your Dracaena. Here are the links: https://www.gardeningknowhow.com/houseplants/dracaena/pruning-dracaena-plants.htm

https://www.gardeningknowhow.com/houseplants/dracaena/dracaena-houseplant-care.htm

I hope these help you!

Air layering is the best way unless you live in the tropics.

Thank you all for your help!

I have one that was given in a flower garden 44 years ago. When it got to tall for the cathedral ceiling I cut off the top and rooted it. It has been broken several times since that by accident and re-roots every time. Still have the original rooted plant that is thriving. A couple of summers I have placed it on an outside porch and the trunk got thicker. No direct sun though. Others can hardly believe how old the original plant it.

Addition to previous comment. I had to re-pot the plant when the roots grew so large they pushed the plant out of the original pot, so may need deeper pot if this happens to yours.

Looks like a Draceana marginata. Looks good and healthy too. Many times you need to prune them to keep them full. 2 or 3 shoots will come out wherever you make your pruning cut. I usually cut one stem at a time and wait to see new growth is coming on then will prune another stem.