When it comes to setting the borders of your image, there are several ways it can go. You can fill the frame as I so often do, the main subject reaching both the left and right borders and quite often the top and bottom ones too. This tends to make images more abstract, more artsy, less illustrative. In not including the surround, you might be asking your viewers to guess both what it is and how large it is in real life.
Sometimes the subject consists of a series of objects one or more of which may be cropped by the edge of the frame. In this case the question is whether part is better than whole. You may not have a choice because of some other framing issue elsewhere on the same side, but if not you may have to decide whether the object can reasonably be represented by the part included. The other consideration is the shapes that this crop creates along the border of the image. It may be that the cropped object is clearly a more interesting shape, or not.
You could choose to run a single object so it just touches the edge in one small area (assuming it isn't rectangle and square to the camera). This will create some shapes defined by the edge of the print and edge of the object - do those enhance the image or not?
It may in fact be better to give the object some breathing room so it doesn't quite touch the edge of the print. There are times that the dramatic straight edge of the print spoils an object that just touches it. Other times there is a claustrophobic feeling when more than one object touches the edge of the print.
Last of all, is it important to include enough surround for the main objects so the surrounding environment becomes an important statement in the image.