Yes, yours looks to be a 'Sky Pencil' Japanese holly bush. It will retain this very upright growth habit and continue to grow taller but not much wider. You only need to trim it if you are trying to limit it to a certain height or if it starts growing into something undesirable like your porch, otherwise no, you don't have to trim it. Trim out dead branches as they appear.
The biggest concern with sky pencil holly is the roots and the soil moisture content. I, and many others have found this cultivar to be particularity sensitive to too much soil moisture as well as dry conditions. So, don't over water it, and don't underwater it.
Here are two articles you may find helpful: