Welcome to the forum
I did a quick test with ImgBurn, and it should be the solution you are searching for. To be sure, however, you can run a test first with a rewritable disc to not waste media
First of all rename all mp3 files with the exact name you want to be shown in the CD. Then run ImgBurn, select the "Write Mode", and then go to menu Tools --> Create CD CUE File.
Drag all mp3 files on the window and then click OK. This will save a CUE file on your hard disk.
Finally, load the CUE file in the Write Mode, insert a CD in the burner, select the burning speed, and start the burning.
As I said, to run a test it is sufficient a rewritable disc. If everything works as you want, then you can use a write once CD to burn the definitive disc