Hi Sasas, from me too.
I agree, your plant is Dragon Tree (Dracaena reflexa var. angustifolia) and cuttings usually take root quite easily. I used to let cuttings lay out to callous over for a few days before potting but my attention span is that of a gnat anymore and it got to the point where I'd forget about them so now when I take cuttings I just immediately stick them back down into the soil of the pot that that the mother plant is in. I keep a small container of rooting hormone powder in my gardening supplies that I use for cuttings but if by chance I've misplaced the rooting powder I also have a small container of ground cinnamon in my plant supplies that works well for cuttings too ... cinnamon is a natural fungicide as well.
~ I'm an old gal who still loves playing in the dirt!
~ Playing in the dirt is my therapy ... and I'm in therapy a lot!