I recently bought this plant and really like it, but I don’t know what it is called. I want to make sure I am able to take good care of it.
The picture is dark, so it is hard to make out the leaf colour. But, based on the shape of the leaf, I would say it is Myrtus communis 'Compacta' AKA Dwarf Myrtle. The leaves are aromatic when crushed. This particular variety of myrtle is very often used to make topiary trees like yours. It is easy to keep trimmed to keep the shape. If you let it go with not trimming it can be come a medium sized shrub. It is hardy to USDA Zone 8-10, but I would not risk it outside in winter if you want to keep the nice clean look. Hardy to zone 8, means the roots will survive to the cold, but the leaves will be significantly damaged by a cold snap. It is like very well drained soil. It does not take well to being over or under watered, so you want to keep it moist, never wet at all times. Avoid cold drafts or radiators. Keep an eye out for spider mite. Washing off the leaves once a month will help keep them from settling in.