I can't say I know for certain, but I can make an educated guess as to why.
The record company that recorded the material has contracts with the performers which will stipulate what each party can and can't do with their recordings and the artist's name or likeness.
Generally the company owns the rights to the recording of the music, but not to the music itself or the artist's name. The record company may have licensed to the course publisher use of the recording, since they own it, but that's all they can license. Since you are speaking of educational material, the course publisher may also be using excerpts of music under the "fair use" doctrine (which is also what allows users on this site to include copyrighted material).
Fair use is not a free license to do whatever you want with material, though. It is to be applied as narrowly as possible, only using what is pertinent to the learning material. Since what is being studied is the opera, not the performer, free use would not extend to the use of the performer's identity.
If, on the other hand, you were studying The Rolling Stones then the band itself would be pertinent to the learning material so free use would cover using their name.
So, the company is not hiding anything, they just don't have the right to give permission to use the performer's name. And if the course publisher happens to know who it is, unless the material is about the performer, free use doesn't allow them to use it either.