Discrepancy between itunes music to sync and what is in the library

What format are these files in and are the tags for each song (piece) correctly filled in?

The tags are the fields of information contained within an audio file, that can be read and edited in your iTunes Library and displayed on your iPhone:

If the tags were not filled in before the track was added to your iTunes Library, it may be that iTunes has assigned a track name by using the filename, which is often the artist, followed by the track title (which seems to be what you're seeing). A second possible issue is that the people who fill in the tags for Classical music do not always follow the correct protocol for track naming. They often put the artist name into the song title. However, at this time, I don't think that is what is happening. I think it's a third possibility; that the artist's name, followed by the song title is all in the song tag (field).

The tracks can be edited in iTunes, as shown above, by selecting the track and clicking on Edit/Song Info. If the problem tracks do not contain the artist name in the artist field, but it is in the song field instead, it's wrong.

In the screenshot above, note the song tag and that it has an up/down select option. Although the option is present in every track, it is used only for Classical music, in order to offer Classical music lovers the additional fields (tags) that they require. (Personally, I don't always make use of it.)

If I tap the song tag, I see the option work name:

Choosing work name, I now see additional tags for classical music:

As you will notice, there is now a field (tag) for movement numbering and name. In your situation though, it's the song tag and the artist tag that you need to check. If the song tag contains the artist name, it's wrong.