What do people typically do with positive log likelihood? I have a probabilistic Machine Learning model that models the data distribution using a multivariate T distribution. This distribution can have density > 1, and so when I compute log likelihood of the data, I sometimes get positive values (meaning likelihood was > 1).
What do researchers typically do in this scenario? Just report the positive log likelihood? Or do they truncate or try to change it in some other way so LL is in (-infinity, 0]?

There is no need to do anything special!  Your confusion might be the same as the one behind Can a probability distribution value exceeding 1 be OK?, so read that.   Also additional useful information in the comments ...
