My cousin brought me a tree, not sure what species it is, Brazillan Rain Tree?
IIRC, the rain trees I’ve seen don’t have as many leaflets as these pictures, but that may be due to being mature bonsai vs. a younger tree like this.
Another possibility is that this is an acacia or mimosa tree.
Does it have thorns?
Might be an acacia, though it looks like a regular old mesquite tree to me. The see pods are the best way to tell.
If it is a mesquite, go really easy on the tap root. They don’t do well if you just cut it off in one shot. It considerably slows down their growth, too. And they lose a lot of their heat hardiness in a pot, so make sure it gets enough water.
I don’t believe it has thorns.
I’m surprised it doesn’t have thorns. Check the nodes in the older growth, though I didn’t really see any in the picture.
How long are the leaflets?
If 1-2 inches, likely Sweet Acacia. If longer than 2 inches, likely Velvet Mesquite. The blooms/pods would be the best way to identify it though.
Either way, loves heat and sun, though partial shade in summer will keep it from burning. Keep it watered in the pot, and don’t let it dry out. Without the deep tap root in the ground, the dry up really quick. That being said, watch out for the tap root to go into the soil if you keep it on the ground. Will back bud on old wood, and it will lose some foliage in winter if it gets cold enough. Will grow considerably slower in the pot. Until the bark starts to form, you shouldn’t have any issues with pests. Once the bark starts to form, they attract beetles like Oncideres rhodosticta (Velcro Bugs) and Pinacate.
Hope this helps. I have some experience with growing Sweet Acacia and Mesquite from seed, though I haven’t had much luck in digging them out the couple of times I’ve tried.
The Phoenix Bonsai Society says this about mesquites…
“Cuttings easily propagated; seems to take pruning well; allow a small stump to remain when a branch is cut off, the stump will dieback; when plant gets too dry will lose leaves quickly; don’t cut the tap root.”