Having your camera perfectly horizontal or vertical is not necessarily something you should always do. Improvise by angling the subject in fun and interesting ways. Try to limit unwanted backgrounds by positioning yourself and angling the camera to minimize background clutter. Try crouching down while having the subject look down toward you. The benefit here is to provide a unique viewpoint, but it also allows you to maximize the possibility of a clean background devoid of random people in the frame.
Skewed angle shot (similar to a dutch angle).
If you are in a large convention center, it works out even better thanks to the ceiling being used as a distant flat background. Does the cosplayer have a large prop or is just generally a big person? Angle their prop or head toward one of the corners of the frame, while framing them overall in a vertical aspect ratio. That way you can still include most of their prop in the frame and you might be surprised how in-your-face interesting the resulting image can be. It’s a good method of maximizing every square inch of the image. When more time is available, take them to a place where you can get above, and sometimes behind them. Have them look back toward your for a unique “I noticed you!” image.