That is a really handy feature to have, especially when you're dealing with files that have multiple language tracks or commentary and you want them to show up correctly in your media player.
Usually, if the option isn't immediately obvious in the main timeline, it's tucked away in the stream selection or "Control" menu. If the Splitter doesn't allow a direct rename within the UI for your specific file format, a quick workaround is to use a tool like MKVToolNix to change the metadata tags before or after the cut - it doesn't require re-encoding, so it stays fast.