So, why are the names different and how do I correct it?
As noted above, the answer likely is: ID3 tags. As a general matter, digital audio players, including the Clip, use metadata embedded in content files to display on the screen. Called ID3 tags, the tags include fields for artist name, file title, year, genre, artist and the like. Under most players, file and folder names do not come into play, as part of this system–this seems to be the situation you are facing.
Oftentimes, the ID3 tags are already filled in when you purchase or otherwise obtain music and audiobook files. But not always, and some of the information might be incorrect or not to your liking. Also, if you rip your own files from CDs, the ID3 tag information needs to be filled in. Nicely, to help with this, Internet databases exist, containing the information, and many rippers will automatically add the information in.
To help with your ID3 tags–either to add the information in or to edit it, in case it is not correct or to your liking–you can use a tag editor. Very good, free editors are available online, such as the well-regarded MP3Tag.
A few additional things to note. First, with the Clip+ and Zip, you actually can navigate by your folders and files and not by the player’s ID3 tag database: if you go to the bottom of the Music listing category, you should see the Folders option, which will let you navigate by your folders and files setup.
Second, you might want to check your USB mode under the player’s Settings. MTP USB mode can sometimes change the names of files when they are transferred to the player–MSC mode tends to be less problematic. And so you may want to set the USB mode to MSC. However, note: a mix of files transferred under the 2 USB modes–MTP and MSC (the Auto mode simply tries to use MTP mode but will fall back to MSC mode, if needed)–can be problematic, as your computer will only show the files that were transferred in the USB mode that you then are connected to your player under. And so, to avoid a mix of USB modes, you can set the player to MTP mode (for example), connect to your computer, transfer your player’s content to your computer, detach the player and set it to MSC mode, and then transfer your content back to the player. Do note as to the USB modes: if you are using any files protected by digital rights management, such as some library content, you need to use MTP mode on your player.
Hope this information is of help–