Why do we use the Hebrew name for Daniel, but Persian names for his companions? Reading the book of Daniel, an odd thing struck me: all four of the men were given Persian names and yet it's only Daniel that is now called by his Hebrew name.

Why is that we call his companions Shadrach, Meshach, and Abednego and not their original names of Hananiah, Mishael, and Azariah?
Since your question is rather general, I'm going to offer a suggestion - a pretty plausible one, but a suggestion. It's probably because they are central to one famous story in the book of Daniel - the fiery furnace - and in that story (which is written in Aramaic) they are given their "Persian" names. After that story, they don't appear in the book at all. In other words, we think "Shadrach, Meshach, and Abednego" immediately in connection to the story of the fiery furnace, and in that story, they have those Persian names.

Daniel, on the other hand, is mentioned  65 times in the book with his Hebrew name, and ten times as Belteshazzar.