Hi & welcome! Agree, Dracaena marginata:
Dragon Tree (Dracaena reflexa var. angustifolia)
This plant looks more bushy because it has more branches. It's normal for the foliage to be in a "poof" at the tip of each branch. I agree, your plant looks great! To get more branches, existing ones can be cut in the hopes that more than 1 branch will replace it, which is often the case, but there are no guarantees. I usually do trimming in late spring through summer, when growth is most vigorous.
A brighter spot can cause the foliage to be upright for a longer period, resulting in a more perky appearance, like this plant:
I repot all of mine every 1-2 yrs. I do it at any time of year except the shortest days of winter. If you find a pancake of roots at the bottom of the root ball, cutting that off will make removing the old soil easier & give roots a chance to grow normally again. This is how bonsai masters are able to keep trees alive for hundreds of years in small pots.
There's a house plant forum here, if you'd like to browse other discussions about Dracaena trees. You can also move this discussion to that forum if you want to by clicking 'suggest a change' in this discussion, in the links between the last post & the box to type a reply.
Dragon Tree (Dracaena reflexa var. angustifolia)