It's all a matter of the name they are commonly known by. That depends on the contexts and languages they are mentioned in, and the conventions used. For example, someone frequently mentioned in ecclesiastic contexts would be more likely to be known by their Latin name.

Furthermore, for many types names there are some conventions adopted by scholars at one point or another - for Roman names, the -us is frequently removed, hence we get "Pompey" and "Livy" rather that POMPEIVS and LIVIVS as they would be known in Latin.

But it can all be quite random. One example would be the Hungarian general we know as John Hunyadi, father of Mathias Corvinus. Now, Corvinus means "the Raven". And what's that in Hungarian? Yep, you guessed it - "Hunyadi". As \u\salarite pointed out, I was completely misremembering this. Mathias Corvinus is, however, known as Hunyadi Matias in Hungarian.