Whatever the species is, it is what gardeners call Myrtle in Lima, Peru. It's a plant that's commonly sold in nurseries here and is found in many gardens. As in most other topics, Peruvians wouldn't get too intellectual about it. It's just the local myrtle. It produces white myrtle flowers.
I bought this one in a nursery because I liked the low ramified structure. Today I took it out of the pot and completely washed the root structure, which was quite small for trying to support such a large bush, no wonder it shed most of its leaves in the hot, dry local summer weather. I decided to chop it to this size and pot it in a plastic basket so it will hopefully develop and ramify its root structure in the next two to four years or so. It has nice, big roots that I think would make beautiful surface roots, particularly if the secondary roots develop well. It also has one higher root which I have not wanted to chop, thinking it would look nice if perhaps some rocks were eventually placed under it, or some cosmetic solution like that. The ramification of the branches is nice. It's the height of a hot El Niño summer here now; the weather will be scorching hot for probably two more months. The apices of the branches were all growing, a new sprout in each and every one of them, so the plant surely has enough of whatever it takes to bud. Under a full plastic cover it will be protected from the drying effect of the heat, and I think it will quite probably bud back very well. Buds develop very well here in the summer if one protects them against the drying effects of the heat.