What is the symbol for uniform distribution in LaTeX? I'm assuming that it is this symbol? Or should I just use a simple U?
There is no standard symbol for a uniform distribution. (The Wikipedia page mentions “U” in italic in text but an image of a calligraphic “U” in summary table; this is inconsistent and non-authoritative.)
So you can use whatever symbol you prefer, preferably following normal conventions for using symbols. Using “U” in italics is certainly acceptable.